Recent zbMATH articles in MSC 76https://www.zbmath.org/atom/cc/762022-01-14T13:23:02.489162ZUnknown authorWerkzeugPreface. Symposium on turbulence structures and aerodynamic heat/ force (STSAHF2018) -- scientific significance of turbulence researchhttps://www.zbmath.org/1475.001162022-01-14T13:23:02.489162ZFrom the text: The Symposium on Turbulence Structures and Aerodynamic Heat/ Force (STSAHF2018) was held in Tianjin, China on 7--9 July 2018.Preface: ``Workshop on the Boltzmann equation, microlocal analysis and related topics''https://www.zbmath.org/1475.001232022-01-14T13:23:02.489162ZFrom the text: This volume of ``RIMS Kôkyûroku Bessatsu'' is the proceedings of the RIMS workshop ``Workshop on the Boltzmann Equation, Microlocal Analysis and Related Topics'', held at the Kyoto University Clock Tower Centennial Hall from May 27 through May 29, 2016. The volume contains research papers and survey articles by invited speakers of the above conference.Deformation of Lie-Poisson algebras and chiralityhttps://www.zbmath.org/1475.170402022-01-14T13:23:02.489162Z"Yoshida, Zensho"https://www.zbmath.org/authors/?q=ai:yoshida.zensho"Morrison, Philip J."https://www.zbmath.org/authors/?q=ai:morrison.philip-j.1Summary: Linearization of a Hamiltonian system around an equilibrium point yields a set of Hamiltonian symmetric spectra: If \(\lambda\) is an eigenvalue of the linearized generator, \(- \lambda\) and \(\overline{\lambda}\) (hence, \(- \overline{\lambda})\) are also eigenvalues -- the former implies a time-reversal symmetry, while the latter guarantees the reality of the solution. However, linearization around a \textit{singular equilibrium point} (which commonly exists in noncanonical Hamiltonian systems) works out differently, resulting in breaking of the Hamiltonian symmetry of spectra; time-reversal asymmetry causes \textit{chirality}. This interesting phenomenon was first found in analyzing the chiral motion of the rattleback, a boat-shaped top having misaligned axes of inertia and geometry [Z. Yoshida et al., Phys. Lett., A 381, No. 34, 2772--2777 (2017; Zbl 1374.81066); erratum ibid. 382, No. 44, 3230 (2018). ]. To elucidate how chiral spectra are generated, we study the three-dimensional Lie-Poisson systems and classify the prototypes of singularities that cause symmetry breaking. The central idea is the \textit{deformation} of the underlying Lie algebra; invoking Bianchi's list of all three-dimensional Lie algebras, we show that the so-called class-B algebras, which are produced by asymmetric deformations of the simple algebra \(\mathfrak{s} \mathfrak{o}(3)\), yield chiral spectra when linearized around their singularities. The theory of deformation is generalized to higher dimensions, including the infinite-dimensional Poisson manifolds relevant to fluid mechanics.
{\copyright 2020 American Institute of Physics}Third-order differential subordinations for multivalent functions in the theory of source-sink dynamicshttps://www.zbmath.org/1475.300372022-01-14T13:23:02.489162Z"Morais, João"https://www.zbmath.org/authors/?q=ai:morais.joao-pedro|morais.joao"Zayed, Hanaa M."https://www.zbmath.org/authors/?q=ai:zayed.hanaa-mousa"Srivastava, Rekha"https://www.zbmath.org/authors/?q=ai:srivastava.rekhaSummary: We propose third-order differential subordination results associated with new admissible classes of multivalent functions defined in the open unit disk on the complex plane. Besides, we investigate the geometric properties of multivalent functions associated with a novel convolution operator. This is done by taking suitable linear combinations of the classical Gaussian hypergeometric function and its derivatives up to third-order and applying the Hadamard product (or convolution) formula for power series. The complex velocity potential and the stream function of two-dimensional potential flow problems over a circular cylinder using both sources with sink and two sources are treated by the methods developed in the present paper. We further determine the fluid flow produced by a single source and construct a univalent function so that the image of source/sink is also source/sink for a given complex potential. Finally, some plot simulations are provided to illustrate the different results of this work.Applications of the duality between the homogeneous complex Monge-Ampère equation and the Hele-Shaw flowhttps://www.zbmath.org/1475.320292022-01-14T13:23:02.489162Z"Ross, Julius"https://www.zbmath.org/authors/?q=ai:ross.julius"Nyström, David Witt"https://www.zbmath.org/authors/?q=ai:witt-nystrom.davidThe authors apply the results from their previous paper [\textit{J. Ross} and \textit{D. W. Nyström}, Publ. Math., Inst. Hautes Étud. Sci. 122, 315--335 (2015; Zbl 1333.32041)] on the relation (via the Legendre transform) between the Hale-Shaw flow on the plane and the Dirichlet problem for the complex homogeneous Monage-Ampère equation on \(\mathbb P ^1 \times \mathbb D\), where \(\mathbb P ^1\) is the complex projetive space of dimension \(1\) with the Fubini-Study form \(\omega\), and \(\mathbb D\) is the unit disc in the plane:
\begin{align*}
&\Phi (\cdot , \tau ) = \phi (\cdot , \tau ), \ \ \ \tau \in \partial \mathbb D, \\
& \pi ^{\ast } \omega + dd^c \Phi \geq 0, \\
&( \pi ^{\ast } \omega + dd^c \Phi )^{2} = 0,
\end{align*}
where \(\pi\) denotes the projection on the first variable and \(\phi (\cdot , \tau )\) is a smooth \(\omega\)-subharmonic function. They provide examples where the solutions fail to be twice differentiable for smooth boundary data. More precisely, given a union, say \(X\), of finitely many points and nonintersecting smooth curve segments in \(\mathbb P ^1 \setminus \{0\} \) there exists a solution \(\phi\) of the problem above which is not twice differentiable at any point of the form \((\tau ^{-1}z, \tau ), z\in X, |\tau |=1\).
The solutions of the Dirichlet problem, when the disc is replaced by the punctured disc, correspond to finding geodesic rays in the space of Kähler potentials on \(\mathbb P ^1\). The authors describe some smooth geodesic rays as Legendre transforms of envelopes produced by the Hale-Shaw flow.
Reviewer: Slawomir Kołodziej (Kraków)Stationary solutions of outflow problem for full compressible Navier-Stokes-Poisson system: existence, stability and convergence ratehttps://www.zbmath.org/1475.340492022-01-14T13:23:02.489162Z"Hong, Hakho"https://www.zbmath.org/authors/?q=ai:hong.hakho"Kim, Jongsung"https://www.zbmath.org/authors/?q=ai:kim.jongsung"Choe, Kwang-Il"https://www.zbmath.org/authors/?q=ai:choe.kwang-ilSummary: In this paper, we study the asymptotic behavior of solution to the initial boundary value problem for the non-isentropic Navier-Stokes-Poisson system in a half line \((0,\infty)\). We consider an outflow problem where the gas blows out the region through the boundary for general gases including ideal polytropic gas. First, we give necessary condition for the existence of stationary solution by use of the center manifold theory. Second, using energy method we show the asymptotic stability of the solutions under assumptions that the boundary value and the initial perturbation is small. Third, we prove that the algebraic and exponential decay of the solution toward supersonic stationary solution is obtained, when the initial perturbation belongs to Sobolev space with algebraic and exponential weight respectively.Long-time behavior for 3D MHD equations with nonlinear dampinghttps://www.zbmath.org/1475.350632022-01-14T13:23:02.489162Z"Song, Xiaoya"https://www.zbmath.org/authors/?q=ai:song.xiaoya"Xiong, Yangmin"https://www.zbmath.org/authors/?q=ai:xiong.yangminSummary: The existence of global attractors is proved for the MHD equations with damping terms \(| u |^{\alpha - 1} u\) and \(| B |^{\beta - 1} B(\alpha, \beta \geqslant 1)\) on a bounded domain \(\Omega \subset \mathbb{R}^3\). First we establish the well-posedness of strong solutions. Then, the continuity of the corresponding semigroup is verified under the assumption \(\alpha, \beta < 5\), which is guided by Gagliardo-Nirenberg inequality. Finally, the system is shown to possess an \((\mathbb{V}, \mathbb{V})\)-global attractor and an \((\mathbb{V}, \text{H}^2)\)-global attractor.On the attractors of for a model describing the motion of weak aqueous polymer solutionshttps://www.zbmath.org/1475.350722022-01-14T13:23:02.489162Z"Kondratyev, Stanislav K."https://www.zbmath.org/authors/?q=ai:kondratyev.stanislav-kSummary: This paper establishes the existence of trajectory and global attractors for a model describing the motion of weak aqueous polymer solutions.On regularity of the 3D MHD equations based on one velocity component in anisotropic Lebesgue spaceshttps://www.zbmath.org/1475.350972022-01-14T13:23:02.489162Z"Guo, Zhengguang"https://www.zbmath.org/authors/?q=ai:guo.zhengguang"Tong, Dongfu"https://www.zbmath.org/authors/?q=ai:tong.dongfu"Wang, Weiming"https://www.zbmath.org/authors/?q=ai:wang.weimingSummary: In this paper we establish a new regularity criterion for the 3D incompressible MHD equations via \(\partial_3 u_3\) and the magnetic field \(b\). By considering different weights in spatial variables, we show in anisotropic Lebesgue spaces if \(\partial_3 u_3\) and \(b\) satisfy certain space-time integrable conditions, which are almost optimal from the scaling invariant point of view, then a weak solution \(( u , b )\) is actually regular. This result gives new insights into the understanding of regularity theory of weak solutions.Global solutions for a simplified shallow elastic fluids modelhttps://www.zbmath.org/1475.351162022-01-14T13:23:02.489162Z"Lu, Yun-guang"https://www.zbmath.org/authors/?q=ai:lu.yunguang"Klingenberg, Christian"https://www.zbmath.org/authors/?q=ai:klingenberg.christian"Rendon, Leonardo"https://www.zbmath.org/authors/?q=ai:rendon.leonardo-a"Zheng, De-Yin"https://www.zbmath.org/authors/?q=ai:zheng.deyinSummary: The Cauchy problem for a simplified shallow elastic fluids model, one \(3 \times 3\) system of Temple's type, is studied and a global weak solution is obtained by using the compensated compactness theorem coupled with the total variation estimates on the first and third Riemann invariants, where the second Riemann invariant is singular near the zero layer depth \(\left(\rho = 0\right)\). This work extends in some sense the previous works of \textit{D. Serre} [J. Differ. Equations 68, 137--168 (1987; Zbl 0627.35062)] and \textit{R. J. LeVeque} and \textit{B. Temple} [Trans. Am. Math. Soc. 288, 115--123 (1985; Zbl 0561.65067)], which provided the global existence of weak solutions for \(2 \times 2\) strictly hyperbolic system and (Heibig, 1994) for \(n \times n\) strictly hyperbolic system with smooth Riemann invariants.The Morse property for functions of Kirchhoff-Routh path typehttps://www.zbmath.org/1475.351272022-01-14T13:23:02.489162Z"Bartsch, Thomas"https://www.zbmath.org/authors/?q=ai:bartsch.thomas.1"Micheletti, Anna Maria"https://www.zbmath.org/authors/?q=ai:micheletti.anna-maria"Pistoia, Angela"https://www.zbmath.org/authors/?q=ai:pistoia.angelaThis article discusses Morse property for functions
\[
f_\Omega(x_1,x_2,\dots,x_N)=f(x_1,x_2,\dots,x_N)-\sum_{j,k=1}^N\lambda_j\lambda_kH_\Omega(x_j,x_k),
\]
where \(\Omega\subset \mathbb{R}^n\) is a bounded domain, \(f\) is a \(C^2\) function defined on a domain in \(\mathbb{R}^{nN}\) and \(H_\Omega\) is the regular part of the Green function on \(\Omega\) object to the Dirichlet condition. The authors establish that for generic domains \(\Omega\), the function \(f_\Omega\) is a Morse function, in the sense that all of its critical points are non-degenerate.
Reviewer: Marius Ghergu (Dublin)On mixed problem of Chaplygin's hodograph equation in hyperbolic domain near the parabolic degenerate linehttps://www.zbmath.org/1475.352002022-01-14T13:23:02.489162Z"Xu, Meng"https://www.zbmath.org/authors/?q=ai:xu.mengSummary: The transonic flow problem is an important one in fluid dynamics or gas dynamics. Local solvability of the mixed problem of Chaplygin's hodograph equation in hyperbolic bounded domains near the degenerate line is considered by using abc method.Interaction of elementary waves for the Aw-Rascle traffic flow model with variable Lane widthhttps://www.zbmath.org/1475.352052022-01-14T13:23:02.489162Z"Zhang, Qinglong"https://www.zbmath.org/authors/?q=ai:zhang.qinglong"Sheng, Wancheng"https://www.zbmath.org/authors/?q=ai:sheng.wanchengThis paper deals with the following model describing the traffic flow on a road with variable width
\[
\begin{cases}
(a\rho )_t + (a\rho u)_x = 0,\\
(a\rho (u + p))_t + (a\rho u(u + p))_x = \rho upa_x ,\\
a_t=0, \end{cases}
\]
where \(\rho, u\) represent the density and the velocity of the vehicular traffic, \(p(\rho)=\rho^\gamma\) is the pressure law (or hesitation function) in traffic flows, and \(a(x)\) represents the lane width which depends on the location.
The authors study the interaction of elementary waves, especially stationary wave interacting with rarefaction wave, shock wave and contact discontinuity.
Reviewer: Giuseppe Maria Coclite (Bari)Well-posedness of evolutionary Navier-Stokes equations with forces of low regularity on two-dimensional domainshttps://www.zbmath.org/1475.352262022-01-14T13:23:02.489162Z"Casas, Eduardo"https://www.zbmath.org/authors/?q=ai:casas.eduardo"Kunisch, Karl"https://www.zbmath.org/authors/?q=ai:kunisch.karlMotivated by optimal control problems in hydrodynamics (where control forces could be measure-valued), the authors study the Navier-Stokes equations in two-dimensional domains \(\Omega\), with the external forces of low regularity: \(L^q((0,T);W^{-1,p}(\Omega))\). Results on the well-posedness of the initial value problem, stability and sensitivity of solutions are proved.
Reviewer: Piotr Biler (Wrocław)Addendum to: ``Ill-posedness for the compressible Navier-Stokes equations with the velocity in \(L^6\) framework''https://www.zbmath.org/1475.352272022-01-14T13:23:02.489162Z"Chen, Jiecheng"https://www.zbmath.org/authors/?q=ai:chen.jiecheng"Wan, Renhui"https://www.zbmath.org/authors/?q=ai:wan.renhuiFrom the text: The authors of the authors' paper [ibid. 18, No. 4, 829--854 (2019; Zbl 1428.35278)] would like to acknowledge that Renhui Wan is the
corresponding author. This has been updated in online version of the original article.Local and parallel finite element algorithms for the time-dependent Oseen equationshttps://www.zbmath.org/1475.352282022-01-14T13:23:02.489162Z"Ding, Qi"https://www.zbmath.org/authors/?q=ai:ding.qi"Zheng, Bo"https://www.zbmath.org/authors/?q=ai:zheng.bo.1|zheng.bo"Shang, Yueqiang"https://www.zbmath.org/authors/?q=ai:shang.yueqiangSummary: Based on two-grid discretizations, local and parallel finite element algorithms are proposed and analyzed for the time-dependent Oseen equations. Using conforming finite element pairs for the spatial discretization and backward Euler scheme for the temporal discretization, the basic idea of the fully discrete finite element algorithms is to approximate the generalized Oseen equations using a coarse grid on the entire domain, and then correct the resulted residual using a fine grid on overlapped subdomains by some local and parallel procedures at each time step. By the theoretical tool of local a priori estimate for the fully discrete finite element solution, error bounds of the approximate solutions from the algorithms are estimated. Numerical results are also given to demonstrate the efficiency of the algorithms.Boundary layer for 3D nonlinear parallel pipe flow of nonhomogeneous incompressible Navier-Stokes equationshttps://www.zbmath.org/1475.352292022-01-14T13:23:02.489162Z"Ding, Shijin"https://www.zbmath.org/authors/?q=ai:ding.shijin"Lin, Zhilin"https://www.zbmath.org/authors/?q=ai:lin.zhilin"Wang, Cuiyu"https://www.zbmath.org/authors/?q=ai:wang.cuiyuSummary: In this paper, we justify the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear parallel pipe flow of nonhomogeneous incompressible Navier-Stokes equations. The convergence for velocity is shown under various Sobolev norms. In addition, the higher-order asymptotic expansions are also considered. And the mathematical validity of the Prandtl boundary layer theory for nonlinear parallel pipe flow is generalized to the nonhomogeneous case.On some model equations of Euler and Navier-Stokes equationshttps://www.zbmath.org/1475.352302022-01-14T13:23:02.489162Z"Du, Dapeng"https://www.zbmath.org/authors/?q=ai:du.dapengSummary: The author proposes a two-dimensional generalization of Constantin-Lax-Majda model. Some results about singular solutions are given. This model might be the first step toward the singular solutions of the Euler equations. Along the same line (vorticity formulation), the author presents some further model equations. He possibly models various aspects of difficulties related with the singular solutions of the Euler and Navier-Stokes equations. Some discussions on the possible connection between turbulence and the singular solutions of the Navier-Stokes equations are made.Three-dimensional shear driven turbulence with noise at the boundaryhttps://www.zbmath.org/1475.352312022-01-14T13:23:02.489162Z"Fan, Wai-Tong Louis"https://www.zbmath.org/authors/?q=ai:fan.wai-tong-louis"Jolly, Michael"https://www.zbmath.org/authors/?q=ai:jolly.michael-s"Pakzad, Ali"https://www.zbmath.org/authors/?q=ai:pakzad.aliStrong stability of 2D viscoelastic Poiseuille-type flowshttps://www.zbmath.org/1475.352322022-01-14T13:23:02.489162Z"Giga, Yoshikazu"https://www.zbmath.org/authors/?q=ai:giga.yoshikazu"Sauer, Jonas"https://www.zbmath.org/authors/?q=ai:sauer.jonas"Schade, Katharina"https://www.zbmath.org/authors/?q=ai:schade.katharina-claraSummary: We investigate \(L^p\)-stability of small viscoelastic Poiseuille-type flows in two dimensions stemming from a model considered in \textit{F.-H. Lin} et al. [Commun. Pure Appl. Math. 58, No. 11, 1437--1471 (2005; Zbl 1076.76006)]. We show global existence and exponential decay of the perturbed flows whenever the initial perturbation and the height of the layer are sufficiently small.Global well-posedness for the stochastic non-Newtonian fluid equations and convergence to the Navier-Stokes equationshttps://www.zbmath.org/1475.352332022-01-14T13:23:02.489162Z"Henandez, Marco"https://www.zbmath.org/authors/?q=ai:henandez.marco"Nguyen, Phuong"https://www.zbmath.org/authors/?q=ai:nguyen.phuong-ha|nguyen.phuong-anh|nguyen.phuong-lan|nguyen.phuong-t-t|nguyen.phuong-hoa|nguyen.phuong-thao|nguyen.phuong-cac|nguyen.phuong-khanh|nguyen.phuong-maiSummary: We establish the existence of global pathwise solutions for the stochastic non-Newtonian incompressible fluid equations in two space dimensions. Moreover, we show that said solutions converge in probability to solutions of the stochastic Navier-Stokes equations in the appropriate limit. Our approach is based on Galerkin approximations and the theory of martingale solutions.About some possible blow-up conditions for the 3-D Navier-Stokes equationshttps://www.zbmath.org/1475.352342022-01-14T13:23:02.489162Z"Houamed, Haroune"https://www.zbmath.org/authors/?q=ai:houamed.harouneSummary: In this paper, we study some conditions related to the question of the possible blow-up of regular solutions to the 3D Navier-Stokes equations. In particular, up to a modification in a proof of a very recent result from \textit{J.-Y. Chemin} et al. [Commun. Partial Differ. Equations 44, No. 12, 1387--1405 (2019; Zbl 1428.35277)], we prove that if one component of the velocity remains small enough in a sub-space of \(\dot{H}^{\frac{1}{2}}\) ``almost'' scaling invariant, then the 3D Navier-Stokes equations are globally wellposed. In a second time, we investigate the same question under some conditions on one component of the vorticity and unidirectional derivative of one component of the velocity in some critical Besov spaces of the form \(L_T^p (\dot{B}_{2, \infty}^{\alpha, \frac{2}{p} - \frac{1}{2} - \alpha})\) or \(L_T^p(\dot{B}_{q, \infty}^{\frac{2}{p} + \frac{3}{q} - 2})\).On the deformation tensor regularity for the Navier-Stokes equations in Lorentz spaceshttps://www.zbmath.org/1475.352352022-01-14T13:23:02.489162Z"Huang, Shiguo"https://www.zbmath.org/authors/?q=ai:huang.shiguo"Ji, Xiang"https://www.zbmath.org/authors/?q=ai:ji.xiangSummary: This paper is concerned with the regularity criteria in terms of the middle eigenvalue of the deformation (strain) tensor \(\mathcal{D}(u)\) to the 3D Navier-Stokes equations in Lorentz spaces. It is shown that a Leray-Hopf weak solution is regular on \((0, T]\) provided that the norm \(\Vert \lambda_2^+ \Vert_{L^{p, \infty }(0,T; L^{q,\infty }(\mathbb{R}^3))}\) with \(2/p + 3/q=2(3/2 < q \leq \infty )\) is small. This generalizes the corresponding works of \textit{J. Neustupa} and \textit{P. Penel} [Adv. Math. Fluid Mech. 237--268, 237--268 (2001; Zbl 1027.35094); C. R., Math., Acad. Sci. Paris 336, No. 10, 805--810 (2003; Zbl 1040.35075); Prog. Nonlinear Differ. Equ. Appl. 61, 197--212 (2005; Zbl 1078.35088)] and \textit{E. Miller} [Arch. Ration. Mech. Anal. 235, No. 1, 99--139 (2020; Zbl 1434.35060)].Some regularity criteria of a weak solution to the 3D Navier-Stokes equations in a domainhttps://www.zbmath.org/1475.352362022-01-14T13:23:02.489162Z"Kim, Jae-Myoung"https://www.zbmath.org/authors/?q=ai:kim.jaemyoungSummary: We give some regularity criterion (of a weak-\(L^p\) Serrin type) of a weak solution to the 3D Navier-Stokes equations in a bounded domain \(\Omega \subset \mathbb{R}^3\) with a smooth boundary. In particular, in case of the half space, we give a regularity condition of a weak solution with respect to a tangential component of the velocity flow vector.Uniqueness and regularity for the 3D Boussinesq system with dampinghttps://www.zbmath.org/1475.352372022-01-14T13:23:02.489162Z"Kim, Yong-Ho"https://www.zbmath.org/authors/?q=ai:kim.yongho"Li, Kwang-Ok"https://www.zbmath.org/authors/?q=ai:li.kwangok"Kim, Chol-Ung"https://www.zbmath.org/authors/?q=ai:kim.chol-ungSummary: This paper is concerned with the Boussinesq system with a damping term and the homogeneous Dirichlet boundary conditions in 3D bounded domains. For a certain range of parameters, we prove that the weak solution is unique if the temperature belongs to \(L^{\infty }(0,T;L^3(\Omega ))\). Also, the global existence of strong solutions to the problem is proved.Approximations of the stochastic 3D Navier-Stokes equations with dampinghttps://www.zbmath.org/1475.352382022-01-14T13:23:02.489162Z"Liu, Hui"https://www.zbmath.org/authors/?q=ai:liu.hui.2|liu.hui.4|liu.hui.3|liu.hui.1"Sun, Chengfeng"https://www.zbmath.org/authors/?q=ai:sun.chengfeng"Xin, Jie"https://www.zbmath.org/authors/?q=ai:xin.jieSummary: The stochastic three-dimensional Navier-Stokes equation with damping is considered in this paper. We show that solutions of three-dimensional stochastic Navier-Stokes equation with damping driven by Brownian motion can be approximated by three-dimensional stochastic Navier-Stokes equation with damping driven by pure jump noise/random kicks on the spaces \(D([0,T],V)\) and \(D([0,T],H)\) for \(3<\beta<5\) with any \(\alpha>0\) and \(\alpha\geq\frac{1}{4}\) as \(\beta=3\).A solution formula and the \(\mathcal{R} \)-boundedness for the generalized Stokes resolvent problem in an infinite layer with Neumann boundary conditionhttps://www.zbmath.org/1475.352392022-01-14T13:23:02.489162Z"Oishi, Kenta"https://www.zbmath.org/authors/?q=ai:oishi.kentaSummary: We consider the generalized Stokes resolvent problem in an infinite layer with Neumann boundary conditions. This problem arises from a free boundary problem describing the motion of incompressible viscous one-phase fluid flow without surface tension in an infinite layer bounded both from above and from below by free surfaces. We derive a new exact solution formula to the generalized Stokes resolvent problem and prove the \(\mathcal{R} \)-boundedness of the solution operator families with resolvent parameter \(\lambda\) varying in a sector \(\Sigma_{\varepsilon , \gamma_0}\) for any \(\gamma_0 > 0\) and \(0 < \varepsilon < \pi /2\), where \(\Sigma_{\varepsilon , \gamma_0} = \{\lambda \in \mathbb{C} \setminus \{0\} | | \arg \lambda | \leq \pi - \varepsilon, | \lambda | > \gamma_0 \} \). As applications, we obtain the maximal \(L_p - L_q\) regularity for the nonstationary Stokes problem and then establish the well-posedness locally in time of the nonlinear free boundary problem mentioned above in \(L_p - L_q\) setting. We make full use of the solution formula to take \(\gamma_0 > 0\) arbitrarily, while in general domains, we only know the \(\mathcal{R} \)-boundedness for \(\gamma_0 \gg 1\) from the result by Shibata. As compared with the case of Neumann-Dirichlet boundary condition studied by Saito, analysis is even harder on account of higher singularity of the symbols in the solution formula.Solutions of a comprehensive dispersion relation for waves at the elastic interface of two viscous fluidshttps://www.zbmath.org/1475.352412022-01-14T13:23:02.489162Z"Rajan, Girish Kumar"https://www.zbmath.org/authors/?q=ai:rajan.girish-kumarSummary: Wave propagation in a system of two arbitrary fluids separated by a contaminated interface in the form of an insoluble monolayer is investigated. The effects of four parameters (density ratio, \(R\); kinematic viscosity ratio, \(V\); Marangoni number, \(P\); and squared wave-Reynolds number, \(\sigma)\) on the solutions of a comprehensive dispersion relation for these waves are analyzed. In the first part of the manuscript, several special cases are considered wherein the comprehensive dispersion relation is modified to a simple polynomial equation and its numerical solutions are obtained for \(\sigma\in[0,1]\). A bifurcation is observed at \(\sigma=\sigma_{\mathrm{b}}\) in two of the solutions in each case; and the system is shown to be overdamped for \(\sigma<\sigma_{\mathrm{b}}\), and underdamped for \(\sigma>\sigma_{\mathrm{b}}\). The relative influences of \(\{R,V,P\}\) on \(\sigma_{\mathrm{b}}\) are also analyzed, and it is found that in general, \( \sigma_{\mathrm{b}}\) is a strong function of \(\{R,V\}\), but a weak function of \(P\). In the second part of the manuscript, numerical solutions of the comprehensive dispersion relation are obtained for waves in a decane-water system, in the limit of \(\{P\gg 1,\sigma\gg 1\}\); and these solutions are classified to correspond to a transverse wave or to a longitudinal wave. The presence of a maximum/minimum in the frequency of oscillation and in the damping rate is observed for the transverse/longitudinal waves. For both the transverse and longitudinal wave modes, the relative deviation of the numerical solution (obtained from the comprehensive dispersion relation) from the respective approximate solution (obtained from a simple dispersion relation) is calculated. The relative deviation, though small, cannot be neglected because it accounts for the effects of elasticity and of capillarity/gravity; and disregarding it in the analyses will fail to yield the inherent maximum/minimum in the frequency of oscillation and in the damping rate for the transverse/longitudinal waves.Existence of global weak solutions for the high frequency and small displacement oscillation fluid-structure interaction systemshttps://www.zbmath.org/1475.352422022-01-14T13:23:02.489162Z"Shen, Lin"https://www.zbmath.org/authors/?q=ai:shen.lin"Wang, Shu"https://www.zbmath.org/authors/?q=ai:wang.shu"Feng, Yuehong"https://www.zbmath.org/authors/?q=ai:feng.yuehongSummary: The purpose of this paper is to study the fluid-structure interaction (FSI) problem which is a simplified model to describe high frequency and small displacement oscillation of elastic structure in fluids. The elastic structure displacement is modeled by a fourth-order nonlinear hyperbolic square equations, the motion of fluid is modeled by the time-dependent incompressible Navier-Stokes equations. We prove the existence of at least one weak solution (global in time) to this problem by compactness method. The result both holds for two-dimensional and three-dimensional cases.A regularity criterion for the Navier-Stokes equations via one diagonal entry of the velocity gradienthttps://www.zbmath.org/1475.352432022-01-14T13:23:02.489162Z"Skalák, Zdeněk"https://www.zbmath.org/authors/?q=ai:skalak.zdenekSummary: We study the conditional regularity of solutions to the Navier-Stokes equations in the three dimensional space. Let \(u=(u_1,u_2,u_3)\) denote the velocity. We impose an additional condition only on one diagonal entry of the velocity gradient, namely \(\partial_3 u_3\), and show, using a technique based on the mixed multiplier theorem and an anisotropic version of the Troisi inequality, that if \(\partial_3 u_3\) lies in the space \(L^\beta (0,T; L^q)\) with suitable \(\beta,q\), then \(u\) is regular on \((0,T]\). Our result improves and extends the analogous results known from the literature.On the compressible viscous barotropic flows subject to large external potential forces in a half space with Navier's boundary conditionshttps://www.zbmath.org/1475.352442022-01-14T13:23:02.489162Z"Song, Changzhen"https://www.zbmath.org/authors/?q=ai:song.changzhen"Zhang, Jianwen"https://www.zbmath.org/authors/?q=ai:zhang.jianwenSummary: This paper is concerned with an initial and boundary value problem of the Navier-Stokes equations for compressible viscous barotropic flow subject to large external potential forces in a half space \(\mathbb{R}_+^3\) with Navier's boundary conditions. The global well-posedness of strong solutions with large oscillations and vacuum is established, provided that the initial energy is suitably small and that the unique steady state is strictly away from vacuum. As a by-product, the stability of stationary solution is obtained.On the steady motion of Navier-Stokes flows past a fixed obstacle in a three-dimensional channel under mixed boundary conditionshttps://www.zbmath.org/1475.352452022-01-14T13:23:02.489162Z"Sperone, Gianmarco"https://www.zbmath.org/authors/?q=ai:sperone.gianmarcoSummary: We analyze the steady motion of a viscous incompressible fluid in a three-dimensional channel containing an obstacle through the Navier-Stokes equations with mixed boundary conditions: the inflow is given by a fairly general datum and the flow is assumed to satisfy a \textit{constant traction} boundary condition on the outlet, together with the standard no-slip assumption on the obstacle and on the remaining walls of the domain. Explicit bounds on the inflow velocity guaranteeing existence and uniqueness of such steady motion are provided after estimating some Sobolev embedding constants and constructing a suitable solenoidal extension of the inlet velocity through the Bogovskii formula. A quantitative analysis of the forces exerted by the fluid over the obstacle constitutes the main application of our results: by deriving a volume integral formula for the drag and lift, explicit upper bounds on these forces are given in terms of the geometrical constraints of the domain.Large time behavior of solutions to a two phase fluid model in \(\mathbb{R}^3\)https://www.zbmath.org/1475.352462022-01-14T13:23:02.489162Z"Tang, Houzhi"https://www.zbmath.org/authors/?q=ai:tang.houzhi"Zhang, Yue"https://www.zbmath.org/authors/?q=ai:zhang.yueSummary: We establish the global existence and large time behavior of a unique classical solution for a two phase fluid model consisting of the compressible isothermal Euler equations coupled with compressible isentropic Navier-Stokes equations via a drag force, provided the initial data is sufficiently small in \(H^4(\mathbb{R}^3)\cap L^1(\mathbb{R}^3)\). The main tools employed in the analysis are the spectrum analysis and energy method. Our results show that the classical solution converges to a given equilibrium state at algebra decay rate.Spontaneous periodic orbits in the Navier-Stokes flowhttps://www.zbmath.org/1475.352472022-01-14T13:23:02.489162Z"van den Berg, Jan Bouwe"https://www.zbmath.org/authors/?q=ai:van-den-berg.jan-bouwe"Breden, Maxime"https://www.zbmath.org/authors/?q=ai:breden.maxime"Lessard, Jean-Philippe"https://www.zbmath.org/authors/?q=ai:lessard.jean-philippe"van Veen, Lennaert"https://www.zbmath.org/authors/?q=ai:van-veen.lennaertIn this paper, the authors propose a computer-assisted approach to the proof of the existence of time-periodic solutions of the Navier-Stokes equations corresponding to a time-independent force.
Consider the Navier-Stokes equations on the three-torus \({\mathbb T}^3\) with size length \(2\pi\):
\[
\begin{cases} \partial_t u+(u\cdot\nabla)u-\nu\Delta u+\nabla p=f \\
\nabla\cdot u=0 \end{cases}\quad\text{in }\mathbb{T}^3\times\mathbb{R},\tag{1}
\]
where \(u=u(x,t)\) and \(p=p(x,t)\) denote the fluid velocity and pressure field (scaled by the fluid -- constant -- density), respectively, \(\nu\) is the coefficient of kinematic viscosity, and \(f=f(x)\) is the given external force which is assumed to be independent of time and having zero spatial average. The problem is whether there exist a period \(T\) and a corresponding analytic periodic solution \((u,p)\) of (1) with period \(T\). This solution corresponds to what the authors call ``spontaneous periodic motion'' as it represents a (non-stationary) time-periodic flow of a fluid driven by a time-independent force.
The existence of spontaneous periodic motions of a fluid governed by the Navier-Stokes equations has been investigated in the following works: [\textit{V. I. Yudovich}, J. Appl. Math. Mech. 35, 587--603 (1971; Zbl 0247.76044); translation from Prikl. Mat. Mekh. 35, 638--655 (1971)], [\textit{G. Iooss}, Arch. Ration. Mech. Anal. 47, 301--329 (1972; Zbl 0258.35057)], [\textit{D. D. Joseph} and \textit{D. H. Sattinger}, Arch. Ration. Mech. Anal. 45, 79--109 (1972; Zbl 0239.76057)], and [\textit{G. P. Galdi}, Arch. Ration. Mech. Anal. 222, No. 1, 285--315 (2016; Zbl 1352.35096)]. These papers are concerned with periodic solutions branching off from a steady state undergoing bifurcation. In contrast, the authors of the present paper provide a proof of the existence of spontaneous periodic motions which are not necessarily ``close'' to a bifurcation point of a steady-state solution.
The strategy of the proof consists in three main steps. The first step is to identify a zero finding problem \(\mathcal F(W)=0\) on the Banach space of geometrically decaying Fourier coefficients. The solution \(W\) corresponds to an angular frequency \(\Omega\) and a time-periodic solution \(\omega\) to the vorticity equation with period \(2\pi/\Omega\). In Lemma 2.5, it is then proved that solutions to \(\mathcal F(W)=0\) correspond to time-periodic solutions \((u,p)\) of (1).
As a second step, consider a numerical approximation \(\bar W\) of \(W\), i.e., \(\mathcal F(\bar W)\approx 0\), then the exact zero \(W\) of \(\mathcal F\) will be found as a fixed point of the operator
\[
T:\; W\mapsto W-D\mathcal F(\bar W)^{-1}\mathcal F(W),
\]
in a neighborhood of \(\bar W\). By Banach fixed point theorem, it is enough to show that \(T\) is a contraction in a ball centered at \(\bar W\). To prove the latter, computable estimates of \(\|D\mathcal F(\bar W)^{-1}\|\) are needed. Instead of working with \(D\mathcal F(\bar W)^{-1}\), the authors construct approximations \(\hat A\) and \(A\) of \(D\mathcal F(\bar W)\) and \(D\mathcal F(\bar W)^{-1}\), respectively, and use these operators to find sufficient conditions to ensure that \(T\) is contraction in a ball centered at \(\bar W\) (Theorem 2.15).
The final step is to derive and implement explicit bounds that meet the hypothesis of Theorem 2.15. Given the high computational cost to evaluate such bounds, the authors use the symmetries of the model to reduce the size of the zero finding problem (Theorem 4.23). The implementation of the bounds in the symmetric setting can be found in [\textit{J. B. van den Berg} et al., MATLAB code for ``Spontaneous periodic orbits in the Navier-Stokes flow'' (2019), \url{https://www.math.vu.nl/~janbouwe/code/navierstokes/}]. The results for time-periodic solutions which are homogeneous in one space variable (more precisely, they are independent of the third space variable and their third component is zero) corresponding to the Taylor-Green forcing
\[
f(x)=\left(\begin{matrix} 2\sin x_1\cos x_2 \\
-2\cos x_1 \sin x_2 \\
0 \end{matrix}\right)
\]
are presented.
Reviewer: Giusy Mazzone (Kingston)Well-posedness of the three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities and far field vacuumhttps://www.zbmath.org/1475.352482022-01-14T13:23:02.489162Z"Xin, Zhouping"https://www.zbmath.org/authors/?q=ai:xin.zhouping"Zhu, Shengguo"https://www.zbmath.org/authors/?q=ai:zhu.shengguoSummary: In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic compressible Navier-Stokes equations is considered. When viscosity coefficients are given as a constant multiple of the density's power \((\rho^\delta\) with \(0<\delta<1)\), based on some analysis of the nonlinear structure of this system, we identify a class of initial data admitting a local regular solution with far field vacuum and finite energy in some inhomogeneous Sobolev spaces by introducing some new variables and initial compatibility conditions, which solves an open problem of degenerate viscous flow partially mentioned by \textit{D. Bresch} et al. [in: Analysis and simulation of fluid dynamics. Collected papers based on the presentations at the conference, Lille, France, June 2005. Basel: Birkhäuser. 15--31 (2007; Zbl 1291.35001)], \textit{Q. Jiu} et al. [J. Math. Fluid Mech. 16, No. 3, 483--521 (2014; Zbl 1308.35165)] and so on. Moreover, in contrast to the classical theory in the case of the constant viscosity, we show that one cannot obtain any global regular solution whose \(L^\infty\) norm of \(u\) decays to zero as time \(t\) goes to infinity.Expansion of a compressible non-barotropic fluid in vacuumhttps://www.zbmath.org/1475.352492022-01-14T13:23:02.489162Z"Yu, Rongfeng"https://www.zbmath.org/authors/?q=ai:yu.rongfengSummary: In this paper, we consider a region occupied by viscous or inviscid compressible magnetohydrodynamic fluids and surrounded by vacuum. It is shown that the fluid region will expand at least linearly in time as soon as there are no singularities. The expanding rate is proportional to initial total energy and is inversely proportional to initial mass. The result indicates an interesting fact that the expansion of the viscous monatomic fluids seems similar to that of the inviscid fluids.Global well-posedness of 2D chemotaxis Euler fluid systemshttps://www.zbmath.org/1475.352502022-01-14T13:23:02.489162Z"Cao, Chongsheng"https://www.zbmath.org/authors/?q=ai:cao.chongsheng"Kang, Hao"https://www.zbmath.org/authors/?q=ai:kang.haoSummary: In this paper we consider a chemotaxis system coupling with the incompressible Euler equations in spatial dimension two, which describing the dynamics of chemotaxis in the inviscid fluid. We establish the regular solutions globally in time under some assumptions on the chemotactic sensitivity.Global bounded weak entropy solutions to the Euler-Vlasov equations in fluid-particle systemhttps://www.zbmath.org/1475.352512022-01-14T13:23:02.489162Z"Cao, Wentao"https://www.zbmath.org/authors/?q=ai:cao.wentao"Jiang, Peng"https://www.zbmath.org/authors/?q=ai:jiang.pengGlobal existence of the three-dimensional compressible Euler equations for generalized Chaplygin gas with dampinghttps://www.zbmath.org/1475.352522022-01-14T13:23:02.489162Z"Cheung, Ka Luen"https://www.zbmath.org/authors/?q=ai:cheung.ka-luenSummary: In this paper, we establish a global existence (GE) result for the three-dimensional compressible Euler equations (CEE) for generalized Chaplygin gas (GCG) with damping. More precisely, by transforming the three-dimensional CEE for GCG with damping to a symmetric hyperbolic system, one shows that the total energy in \(H^3\) is strictly decaying with time for any sufficiently small initial data. As a result, the GE result follows from the local well-posedness of the system in \(H^3\). This gives the first GE result relating to the three-dimensional CEE.Existence of global bounded smooth solutions for the one-dimensional nonisentropic Euler systemhttps://www.zbmath.org/1475.352542022-01-14T13:23:02.489162Z"Lai, Geng"https://www.zbmath.org/authors/?q=ai:lai.geng"Zhao, Qing"https://www.zbmath.org/authors/?q=ai:zhao.qingSummary: We study the existence of global bounded smooth solutions to the one-dimensional (1D) nonisentropic Euler system with large initial data. We derive a group of characteristic decompositions for the 1D nonisentropic Euler system. Using these characteristic decompositions, we find some sufficient conditions on the initial data to obtain the existence of global bounded classical solutions to the Cauchy problem. By the method of characteristic decomposition, we also give a type of large initial data to show the formation of singularity for the 1D nonisentropic Euler system.Continuous data assimilation for the three-dimensional simplified Bardina model utilizing measurements of only two components of the velocity fieldhttps://www.zbmath.org/1475.352552022-01-14T13:23:02.489162Z"Anh, Cung The"https://www.zbmath.org/authors/?q=ai:cung-the-anh."Bach, Bui Huy"https://www.zbmath.org/authors/?q=ai:bach.bui-huyThe simplified Bardina model is a modification of the Navier-Stokes equations for the velocity \(u\), which deals with the quantity \(v=u-\alpha^2\Delta u\), so for \(\alpha=0\) coincides with the original Navier-Stokes system. The authors obtain estimates of the difference between the approximating solution and the unknown reference solution corresponding to measurements of two of three components of the velocity. Three different interpolant operators are studied as inputs to the algorithm leading to an approximate solution.
Reviewer: Piotr Biler (Wrocław)A novel 3D model for non-Newtonian fluid flows in a pipe networkhttps://www.zbmath.org/1475.352562022-01-14T13:23:02.489162Z"Baranovskii, Evgenii S."https://www.zbmath.org/authors/?q=ai:baranovskii.evgenii-sergeevichSummary: In this paper, we propose a novel mathematical model that describes steady-state 3D flows of a non-Newtonian fluid with shear-dependent viscosity in a pipe network. Our approach is based on the rejection of averaging of the velocity field and the application of conjugation conditions that provide the mass balance for interior joints of the network. Using boundary conditions involving the pressure, we formulate the corresponding boundary value problem and introduce the concept of weak solutions by integral indentities. The main result of the work is an existence theorem in the class of weak solutions for large data. The proof of this result is performed with the help of the Galerkin procedure, methods of the topological degree theory, the technique of monotone operators as well as compactness arguments.Unique weak solutions of the \(d\)-dimensional micropolar equation with fractional dissipationhttps://www.zbmath.org/1475.352572022-01-14T13:23:02.489162Z"Ben Said, Oussama"https://www.zbmath.org/authors/?q=ai:ben-said.oussama"Wu, Jiahong"https://www.zbmath.org/authors/?q=ai:wu.jiahongSummary: This article examines the existence and uniqueness of weak solutions to the \(d\)-dimensional micropolar equations \((d=2\) or \(d=3)\) with general fractional dissipation \((- \Delta)^{\alpha} u\) and \((- \Delta)^{\beta} w\). The micropolar equations with standard Laplacian dissipation model fluids with microstructure. The generalization to include fractional dissipation allows simultaneous study of a family of equations and is relevant in some physical circumstances. We establish that, when \(\alpha \geq \frac{ 1}{ 2}\) and \(\beta \geq \frac{ 1}{ 2} \), any initial data \((u_0,w_0)\) in the critical Besov space \(u_0 \in B_{2 , 1}^{1 + \frac{ d}{ 2} - 2 \alpha}( \mathbb{R}^d)\) and \(w_0 \in B_{2 , 1}^{1 + \frac{ d}{ 2} - 2 \beta}( \mathbb{R}^d)\) yields a unique weak solution. For \(\alpha \geq 1\) and \(\beta =0\), any initial data \(u_0 \in B_{2 , 1}^{1 + \frac{ d}{ 2} - 2 \alpha}( \mathbb{R}^d)\) and \(w_0 \in B_{2 , 1}^{\frac{ d}{ 2}}( \mathbb{R}^d)\) also leads to a unique weak solution as well. The regularity indices in these Besov spaces appear to be optimal and can not be lowered in order to achieve the uniqueness. Especially, the 2D micropolar equations with the standard Laplacian dissipation, namely, \( \alpha =\beta =1\), have a unique weak solution for \(( u_0, w_0) \in B_{2 , 1}^0\). The proof involves the construction of successive approximation sequences and extensive a priori estimates in Besov space settings.Dispersive of propagation wave solutions to unidirectional shallow water wave Dullin-Gottwald-Holm system and modulation instability analysishttps://www.zbmath.org/1475.352582022-01-14T13:23:02.489162Z"Bilal, M."https://www.zbmath.org/authors/?q=ai:bilal.muhammad"Seadawy, Aly R."https://www.zbmath.org/authors/?q=ai:seadawy.aly-r"Younis, M."https://www.zbmath.org/authors/?q=ai:younis.muhammad"Rizvi, S. T. R."https://www.zbmath.org/authors/?q=ai:rizvi.syed-tahir-raza"Zahed, Hanadi"https://www.zbmath.org/authors/?q=ai:zahed.hanadiSummary: This article possesses modulation instability (MI) analysis and new exact wave solutions to unidirectional Dullin-Gottwald-Holm (DGH) system that describes the prorogation of waves in shallow water. The exact wave solutions in single and combined form like shock, singular, and shock-singular are extracted by means of an innovative integration norm, namely, \( \left( G^{\prime} / G^2\right)\)-expansion scheme. The periodic and plane wave solutions are also emerged. The constraint conditions which ensure the existence of solutions are discussed as well. Moreover, the choice of suitable parameters gives the three-dimensional and two-dimensional sketches, and furthermore, their contour plots are also drawn.The Darcy problem with porosity depending exponentially on the pressurehttps://www.zbmath.org/1475.352592022-01-14T13:23:02.489162Z"Birhanu, Zerihun Kinfe"https://www.zbmath.org/authors/?q=ai:birhanu.zerihun-kinfe"Mengesha, Tadele"https://www.zbmath.org/authors/?q=ai:mengesha.tadele"Salgado, Abner J."https://www.zbmath.org/authors/?q=ai:salgado.abner-jSummary: We consider the flow of a viscous incompressible fluid through a porous medium. We allow the permeability of the medium to depend exponentially on the pressure and provide an analysis for this model. We study a splitting formulation where a convection diffusion problem is used to define the permeability, which is then used in a linear Darcy equation. We also study a discretization of this problem, and provide an error analysis for it.The evolution dam problem for a compressible fluid with nonlinear Darcy's law and Dirichlet boundary conditionhttps://www.zbmath.org/1475.352602022-01-14T13:23:02.489162Z"Bousselsal, Mahmoud"https://www.zbmath.org/authors/?q=ai:bousselsal.mahmoud"Zaouche, Elmehdi"https://www.zbmath.org/authors/?q=ai:zaouche.elmehdiSummary: In this paper, we consider the evolution dam problem \((P)\) related to a compressible fluid flow governed by a generalized nonlinear Darcy's law with Dirichlet boundary conditions on some part of the boundary. We establish existence of a solution for this problem. We choose a convenient regularized problem \((P_\epsilon)\) for which we prove the existence and uniqueness of solution using the comparison Lemma 2.1 and the Schauder fixed-point theorem. Then, we pass to the limit, when \(\epsilon\) goes to 0, to get a solution for our problem. Moreover, we will see another approach for the incompressible case where we pass to the limit in \((P)\), when \(\alpha\) goes to 0, to get a solution.Closed solutions of some boundary-value problems of filtration-consolidation dynamics within the fractured-fractal approachhttps://www.zbmath.org/1475.352612022-01-14T13:23:02.489162Z"Bulavatsky, V. M."https://www.zbmath.org/authors/?q=ai:bulavatskyi.volodymyr-mSummary: The autor constructs a fractured-fractal mathematical model of the dynamics of the process of filtration consolidation of a soil medium, a model of the dynamics of the process of filtration consolidation of massifs of fractal structure, taking into account creep of the soil skeleton (direct and inverse retrospective problems), and a fractured-fractal mathematical model of the dynamics of the process of filtration consolidation of soil media saturated with saline solutions. Within the framework of these models, statements have been made and closed solutions have been obtained for some boundary-value problems, one-dimensional with respect to the geometric variable, on the consolidation of water-saturated soil massifs of fractal structure under time nonlocality of the compaction process.On incompressible heat-conducting viscoelastic rate-type fluids with stress-diffusion and purely spherical elastic responsehttps://www.zbmath.org/1475.352622022-01-14T13:23:02.489162Z"Bulíček, Miroslav"https://www.zbmath.org/authors/?q=ai:bulicek.miroslav"Málek, Josef"https://www.zbmath.org/authors/?q=ai:malek.josef"Průša, Vít"https://www.zbmath.org/authors/?q=ai:prusa.vit"Süli, Endre"https://www.zbmath.org/authors/?q=ai:suli.endre-eThe paper provides the existence of weak solutions to a system modeling flows of incompressible heat-conducting viscoelastic rate-type fluids with stress-diffusion. These fluids are characterized by a diffusive contribution that takes origin in a specific term of the stress tensor and it is called stress-diffusion term. Therefore the system is made by: the governing equations for the flow of an incompressible Oldroyd-B fluid with a stress-diffusion term; an evolution equation for the temperature. Previous mathematical results concern the isothermal case. This work analyzes the general non-isothermal case and it is a step towards the analysis of the full model (some simplifying assumption is made on the stress tensor).The authors study weak solutions, choosing the total energy (instead of the temperature alone) as one of the variables of the weak formulation of the system.
Reviewer: Roberta Bianchini (Roma)Linear evolution of IGW structures in the ionospheri plasma at interaction with shear flowshttps://www.zbmath.org/1475.352632022-01-14T13:23:02.489162Z"Chargazia, Khatuna"https://www.zbmath.org/authors/?q=ai:chargazia.khatuna"Kharshiladze, Oleg"https://www.zbmath.org/authors/?q=ai:kharshiladze.oleg-a"Kvaratskhelia, Diana"https://www.zbmath.org/authors/?q=ai:kvaratskhelia.diana"Zimbardo, Gaetano"https://www.zbmath.org/authors/?q=ai:zimbardo.gaetano"Sorriso-Valvo, Luca"https://www.zbmath.org/authors/?q=ai:sorriso-valvo.lucaSummary: Theoretical explanation intensification of low frequency (LF) internal gravity waves (IGW) is presented. The method used is based on generalizing results on shear flow phenomena from the hydrodynamics community. In the 1990s, it was realized that fluctuation modes of spectrally stable nonuniform sheared flows are non-normal. That is, the linear operators of the flows modal analysis are non-normal and the corresponding eigenmodes are not orthogonal. The non-normality results in linear transient growth with bursts of the perturbations and the mode coupling, which causes the amplification of LF IG waves shear flow driven ionospheric plasma and generation of the higher frequency oscillations. Transient growth substantially exceeds the growth of the classical dissipative trapped-particle instability of the system.Regularity criteria for the 3D magnetic Bénard equations without thermal diffusion in terms of pressurehttps://www.zbmath.org/1475.352642022-01-14T13:23:02.489162Z"Chen, Dongxiang"https://www.zbmath.org/authors/?q=ai:chen.dongxiang"Jian, Fangfang"https://www.zbmath.org/authors/?q=ai:jian.fangfang"Chen, Xiaoli"https://www.zbmath.org/authors/?q=ai:chen.xiaoliSummary: In this paper, the authors obtain some new blow-up criteria for the smooth solutions to the three-dimensional magnetic Bénard equations without thermal diffusion in terms of pressure. We prove that if \(\pi \in L^2 \left(0 ,T ;L^{\frac{3}{r}} (\mathbb{R}^3)\right)\) with \(0 < r \leq 1\), then the strong solutions \((u, b, \theta )\) to the magnetic Bénard equations can be extended beyond time \(t = T\). Meanwhile, we also show that provided that \(\nabla \pi \in L^{\frac{9 - 2 r}{2 r}} \left(0, T ;L^{\frac{3}{r}} (\mathbb{R}^3 )\right)\) with \(0 < r \leq 1\), the solutions \((u, b, \theta )\) can also be extended smoothly beyond \(t = T\). Finally, we also obtain the regularity criteria on Morrey space, multiplier space, BMO space, and Besov space by imposing some growth conditions only on the pressure field.On the slightly perturbed de Gregorio model on \(S^1\)https://www.zbmath.org/1475.352652022-01-14T13:23:02.489162Z"Chen, Jiajie"https://www.zbmath.org/authors/?q=ai:chen.jiajieSummary: It is conjectured that the generalization of the Constantin-Lax-Majda model (gCLM) \( \omega_t + a u\omega_x = u_x \omega \), due to \textit{H. Okamoto} et al. [Discrete Contin. Dyn. Syst. 34, No. 8, 3155--3170 (2014; Zbl 1292.35237)], can develop a finite time singularity from smooth initial data for \(a < 1\). For the endpoint case where \(a\) is close to and less than 1, we prove finite time asymptotically self-similar blowup of gCLM on a circle from a class of smooth initial data. For the gCLM on a circle with the same initial data, if the strength of advection \(a\) is slightly larger than 1, we prove that the solution exists globally with \(|| \omega (t)||_{H^1}\) decaying in a rate of \(O(t^{-1})\) for large time. The transition threshold between two different behaviors is \(a=1\), which corresponds to the De Gregorio model.A quasilinear system related with the asymptotic equation of the nematic liquid crystal's director fieldhttps://www.zbmath.org/1475.352672022-01-14T13:23:02.489162Z"Dias, João-Paulo"https://www.zbmath.org/authors/?q=ai:dias.joao-pauloSummary: In this paper, the author studies the local existence of strong solutions and their possible blow-up in time for a quasilinear system describing the interaction of a short wave induced by an electron field with a long wave representing an extension of the motion of the director field in a nematic liquid crystal's asymptotic model introduced in
[\textit{R. A. Saxton}, Contemp. Math. 100, 325--330 (1989; Zbl 0702.35180)]
and
[\textit{J. K. Hunter} and \textit{R. Saxton}, SIAM J. Appl. Math. 51, No. 6, 1498--1521 (1991; Zbl 0761.35063)]
and studied in
[\textit{J. K. Hunter} and \textit{Y. Zheng}, Arch. Ration. Mech. Anal. 129, No. 4, 305--353, 355--383 (1995; Zbl 0834.35085)]
and in
[\textit{P. Zhang} and \textit{Y. Zheng}, Asymptotic Anal. 18, No. 3--4, 307--327 (1998; Zbl 0935.35031)]
and, more recently, in
[\textit{A. Bressan} et al., Arch. Ration. Mech. Anal. 183, No. 1, 163--185 (2007; Zbl 1168.35026)].Asymptotic behavior of solutions to a class of incompressible third grade fluid equationshttps://www.zbmath.org/1475.352682022-01-14T13:23:02.489162Z"Duan, Ning"https://www.zbmath.org/authors/?q=ai:duan.ningSummary: We study the asymptotic behavior of incompressible third grade fluid equations. First, by using the pure energy method, we obtain the global well-posedness of strong solutions provided that the initial data is sufficiently small. Second, on the basis of negative Sobolev norm estimates, we establish the optimal decay rates of strong solutions.Canonical system of equations for 1D water waveshttps://www.zbmath.org/1475.352692022-01-14T13:23:02.489162Z"Dyachenko, Alexander I."https://www.zbmath.org/authors/?q=ai:dyachenko.aleksandr-ivanovichThis paper is based on an earlier work by the author and his collaborators on unidirectional water waves governed by an equation, the so called super compact equation for water waves. Using a specific property of the four-wave interaction of water waves in the one dimensional wave field and a particular canonical transformation, the author presents a simplified version of a pair of equations. This simplified system includes interaction terms, between counter-streaming waves, and is referred to as the canonical system of equations for one-dimensional water waves that describes wave propagation in opposite directions along the x-axis exhibiting nonlinearity; from this system of equations, an exact and fairly simple equation for a standing wave is obtained. Under certain initial conditions, it is shown that the canonical system reduces to super compact equation.
Reviewer: Vishnu Dutt Sharma (Ghandinagar)Energy transfer by internal-gravity wavy structures in the upper atmosphere with the shear flowhttps://www.zbmath.org/1475.352702022-01-14T13:23:02.489162Z"Elbakidze, Khatuna"https://www.zbmath.org/authors/?q=ai:elbakidze.khatuna"Kharshiladze, Oleg"https://www.zbmath.org/authors/?q=ai:kharshiladze.oleg-a"Zimbardo, Gaetano"https://www.zbmath.org/authors/?q=ai:zimbardo.gaetanoSummary: The nonlinear dynamics of internal gravity waves (IGW) in stably stratified dissipative ionosphere with non-uniform zonal wind (shear flow) is studied. Due to the nonlinear mechanism nonlinear solitary, strongly localized IGW vortex structures can be formed. Therefore, a new degree of freedom of the system and accordingly, the path of evolution of disturbances appear in a medium with shear flow. Depending on the type of shear ow velocity profile the nonlinear IGW structures can be the pure monopole vortices, the transverse vortex chain or the longitudinal vortex street in the background of non-uniform zonal wind. Accumulation of these vortices in the ionosphere medium can create the strongly turbulent state.Uniform estimates for a compressible full MHD-\(P1\) approximate model arising in radiation MHDhttps://www.zbmath.org/1475.352712022-01-14T13:23:02.489162Z"Fan, Jishan"https://www.zbmath.org/authors/?q=ai:fan.jishan"Wang, Peng"https://www.zbmath.org/authors/?q=ai:wang.peng.1|wang.peng|wang.peng.2"Zhou, Yong"https://www.zbmath.org/authors/?q=ai:zhou.yong.1Summary: We prove the uniform estimates of strong solutions to a compressible full MHD-\(P1\) approximate model arising in radiation magnetohydrodynamics.Regularity criteria of the density-dependent incompressible ideal Boussinesq and liquid crystals modelhttps://www.zbmath.org/1475.352722022-01-14T13:23:02.489162Z"Fan, Jishan"https://www.zbmath.org/authors/?q=ai:fan.jishan"Zhang, Zujin"https://www.zbmath.org/authors/?q=ai:zhang.zujinSummary: In this paper, we prove some regularity criteria for the density-dependent incompressible Boussinesq and liquid crystals model. The Kato-Ponce type commutator estimates play a key role.A new regularity criterion of weak solutions to the 3D micropolar fluid flows in terms of the pressurehttps://www.zbmath.org/1475.352732022-01-14T13:23:02.489162Z"Gala, Sadek"https://www.zbmath.org/authors/?q=ai:gala.sadek"Ragusa, Maria Alessandra"https://www.zbmath.org/authors/?q=ai:ragusa.maria-alessandra"Théra, Michel"https://www.zbmath.org/authors/?q=ai:thera.michel-aSummary: In this study, we establish a new regularity criterion of weak solutions to the three-dimensional micropolar fluid flows by imposing a critical growth condition on the pressure field.Lower bound of decay rate for higher order derivatives of solution to the compressible quantum magnetohydrodynamic modelhttps://www.zbmath.org/1475.352742022-01-14T13:23:02.489162Z"Gao, Jincheng"https://www.zbmath.org/authors/?q=ai:gao.jincheng"Lyu, Zeyu"https://www.zbmath.org/authors/?q=ai:lyu.zeyu"Yao, Zheng-An"https://www.zbmath.org/authors/?q=ai:yao.zhenganSummary: The lower bounds of decay rates for global solution to the compressible viscous quantum magnetohydrodynamic model in three-dimensional whole space under the \(H^5 \times H^4 \times H^4\) framework are investigated in this paper. We first show that the lower bound of decay rate for the solution converging to constant equilibrium state \((1, 0, 0)\) in \(L^2\)-norm is \((1 + t)^{- \frac{3}{4}}\) when the initial data satisfy some low-frequency assumption. Moreover, we prove that the lower bound of decay rate of \(k(k \in [1, 3])\) order spatial derivative for the solution converging to constant equilibrium state \((1, 0, 0)\) in \(L^2\)-norm is \((1 + t)^{- \frac{3 + 2k}{4}}\). Then, we show that the lower bound of decay rate for the time derivatives of density and velocity is \((1 + t)^{- \frac{5}{4}} \), but the lower bound of decay rate for the time derivative of magnetic field converging to zero in \(L^2\)-norm is \((1 + t)^{- \frac{7}{4}} \).Derivation of the Batchelor-Green formula for random suspensionshttps://www.zbmath.org/1475.352752022-01-14T13:23:02.489162Z"Gérard-Varet, David"https://www.zbmath.org/authors/?q=ai:gerard-varet.davidSummary: This paper is dedicated to the effective viscosity of suspensions without inertia, at low solid volume fraction \(\phi\). The goal is to derive rigorously a \(o(\phi^2)\) formula for the effective viscosity. In our works with \textit{M. Hillairet} [Arch. Ration. Mech. Anal. 238, No. 3, 1349--1411 (2020; Zbl 1454.76101); ``On the correction to Einstein's formula for the effective viscosity'', Preprint, \url{arXiv:2004.05601}], such formula was given for rigid spheres satisfying the strong separation assumption \(d_{\min}\geq c\phi^{-\frac{1}{3}}r\), where \(d_{\min}\) is the minimal distance between the spheres and \(r\) their radius. It was then applied to both periodic and random configurations with separation, to yield explicit values for the \(O(\phi^2)\) coefficient. We consider here complementary (and certainly more realistic) random configurations, satisfying softer assumptions of separation, and long range decorrelation. We justify in this setting the famous Batchelor-Green formula [\textit{G. K. Batchelor} and \textit{J. T. Green}, J. Fluid Mech. 56, 401--427 (1972; Zbl 0246.76108)]. Our result applies for instance to hardcore Poisson point process with almost minimal hardcore assumption \(d_{\min}>(2+\varepsilon)r\), \(\varepsilon>0\).A time domain approach for the exponential stability of a linearized compressible flow-structure PDE systemhttps://www.zbmath.org/1475.352762022-01-14T13:23:02.489162Z"Geredeli, Pelin Guven"https://www.zbmath.org/authors/?q=ai:geredeli.pelin-guvenSummary: This work is motivated by a longstanding interest in the long time behavior of flow-structure interaction (FSI) PDE dynamics. We consider a linearized compressible flow structure interaction (FSI) PDE model with a view of analyzing the stability properties of both the compressible flow and plate solution components. In our earlier work, we gave an answer in the affirmative to question of uniform stability for finite energy solutions of said compressible flow-structure system, by means of a ``frequency domain'' approach. However, the frequency domain method of proof in that work is not ``robust'' (insofar as we can see), when one wishes to study longtime behavior of solutions of compressible flow-structure PDE models, which track the appearance of the ambient state onto the boundary interface. Nor is a frequency domain approach in this earlier work availing when one wishes to consider the dynamics, in long time, of solutions to physically relevant nonlinear versions of the compressible flow-structure PDE system under present consideration (e.g., the Navier-Stokes nonlinearity in the PDE flow component or a nonlinearity of Berger/Von Karman type in the plate equation). Accordingly, in the present work, we operate in the time domain by way of obtaining the necessary energy estimates, which culminate in an alternative proof for the uniform stability of finite energy compressible flow-structure solutions. Since there is a need to avoid steady states in our stability analysis, as a prerequisite result, we also show here that zero is an eigenvalue for the generators of flow-structure systems, whether the material derivative term be absent or present. Moreover, we provide a clean characterization of the (one dimensional) zero eigenspace, with or without material derivative, under an appropriate assumption on the underlying ambient vector field.Long time behavior of a two fluid modelhttps://www.zbmath.org/1475.352772022-01-14T13:23:02.489162Z"Ghoul, Tej-eddine"https://www.zbmath.org/authors/?q=ai:ghoul.tej-eddine"Ibrahim, Slim"https://www.zbmath.org/authors/?q=ai:ibrahim.slim"Shen, Shengyi"https://www.zbmath.org/authors/?q=ai:shen.shengyiSummary: We consider a two fluid model which describes the motion of two charged particles in a strict neutral incompressible plasma. In this paper we mainly study the stability of the solution around zero given that the initial data is small and has sufficient regularity. In this paper we show that our system is a system of regularity-loss and the \(L^2\) norm of lower derivatives of the solution decays with a rate.On the well-posedness of the damped time-harmonic Galbrun equation and the equations of stellar oscillationshttps://www.zbmath.org/1475.352782022-01-14T13:23:02.489162Z"Halla, Martin"https://www.zbmath.org/authors/?q=ai:halla.martin"Hohage, Thorsten"https://www.zbmath.org/authors/?q=ai:hohage.thorstenExistence and weak-strong uniqueness of solutions to the Cahn-Hilliard-Navier-Stokes-Darcy system in superposed free flow and porous mediahttps://www.zbmath.org/1475.352792022-01-14T13:23:02.489162Z"Han, Daozhi"https://www.zbmath.org/authors/?q=ai:han.daozhi"He, Xiaoming"https://www.zbmath.org/authors/?q=ai:he.xiaoming.1"Wang, Quan"https://www.zbmath.org/authors/?q=ai:wang.quan"Wu, Yanyun"https://www.zbmath.org/authors/?q=ai:wu.yanyunSummary: We study a diffuse interface model for two-phase flows of similar densities in superposed free flow and porous media. The model consists of the Navier-Stokes-Cahn-Hilliard system in free flow and the Darcy-Cahn-Hilliard system in porous media coupled through a set of domain interface boundary conditions. These domain interface boundary conditions include the nonlinear Lions interface condition and the linear Beavers-Joseph-Saffman-Jones interface condition. We establish global existence of weak solutions in three dimension. We also show that the strong solution if exists agrees with the weak solutions.Generalized resolvent of the Stokes problem with Navier-type boundary conditionshttps://www.zbmath.org/1475.352802022-01-14T13:23:02.489162Z"Hind, Al Baba"https://www.zbmath.org/authors/?q=ai:hind.al-baba"Jabbour, Antonia"https://www.zbmath.org/authors/?q=ai:jabbour.antoniaSummary: We study in this paper the generalized resolvent of the Stokes problem with Navier-type boundary conditions.
For the entire collection see [Zbl 1448.65007].The inviscid limit of third-order linear and nonlinear acoustic equationshttps://www.zbmath.org/1475.352822022-01-14T13:23:02.489162Z"Kaltenbacher, Barbara"https://www.zbmath.org/authors/?q=ai:kaltenbacher.barbara"Nikolić, Vanja"https://www.zbmath.org/authors/?q=ai:nikolic.vanjaThis work analyzes a model describing the evolution of sound waves through thermally relaxing media as the diffusivity of sound vanishes. The considered sound wave equation is third order in time and two kinds of nonlinearities, with different physical interpretations, are taken into account. The authors investigate the behavior of the solutions as the ``diffisivity of sound'' \(\delta\) vanishes. In other words, this paper deals with the vanishing sound diffusivity limit in thermally relaxing fluids or gases. It shows that sufficiently smooth solutions of these equations converge in the energy norm to the solutions of the corresponding inviscid models at a linear rate. The mathematical analysis is also complemented with numerical simulations.
Reviewer: Roberta Bianchini (Roma)Numerical simulation for the mixed convective flow of non-Newtonian fluid with activation energy and entropy generationhttps://www.zbmath.org/1475.352832022-01-14T13:23:02.489162Z"Khan, Muhammad Ijaz"https://www.zbmath.org/authors/?q=ai:khan.muhammad-ijaz"Alzahrani, Faris"https://www.zbmath.org/authors/?q=ai:alzahrani.faris-saeedSummary: Here, mathematical modeling is performed for the nonlinear mixed convection in dissipative convective flow of micropolar fluid towards a stretched surface. Mixed convection occurs when both forced and natural convection mechanisms act together. Mixed convection problems are categorized by Grashof number. This is also addressed as situations where both buoyant and pressure forces interact. Slip condition is considered at the boundary for the velocity. Magnetohydrodynamics (MHD) fluid is considered. Novel features of nanofluids like Brownian motion and thermophoresis diffusions are further addressed. Convective condition is imposed at the stretched boundary. Concentration of material particles is discussed with activation energy. Nonlinear partial differential equations are converted into ordinary ones via appropriate similarity transformations. The velocity, temperature, concentration, skin friction, Nusselt number, and entropy generation are discussed numerically with the help of built-in-shooting method. Our obtained outcomes show that the velocity of material particles reduces against larger slip parameter and micropolar parameter. Temperature enhances for larger thermal Biot and Eckert numbers. Concentration of fluid particles is more versus solutal Biot number and activation energy parameter. Furthermore, entropy rate increases for higher values of micropolar fluid parameter and activation energy parameter while it declines against slip parameter.On local strong solutions to the Cauchy problem of two-dimensional nonhomogeneous Navier-Stokes-Korteweg equations with vacuumhttps://www.zbmath.org/1475.352842022-01-14T13:23:02.489162Z"Li, Huanyuan"https://www.zbmath.org/authors/?q=ai:li.huanyuanSummary: In this paper, we consider the Cauchy problem of nonhomogeneous incompressible Navier-Stokes-Korteweg equations on the two-dimensional space with vacuum as the far field density. We establish the local existence and uniqueness of strong solutions to the 2D Cauchy problem of nonhomogeneous incompressible Navier-Stokes-Korteweg equations provided the initial density decays not too slow at infinity.Approximate controllability of second-grade fluidshttps://www.zbmath.org/1475.352852022-01-14T13:23:02.489162Z"Ngo, Van-Sang"https://www.zbmath.org/authors/?q=ai:ngo.van-sang"Raugel, Geneviève"https://www.zbmath.org/authors/?q=ai:raugel.genevieveSummary: This paper deals with the controllability of the second-grade fluids, a class of non-Newtonian of differential type, on a two-dimensional torus. Using the method of \textit{A. A. Agrachev} and \textit{A. V. Sarychev} [J. Math. Fluid Mech. 7, No. 1, 108--152 (2005; Zbl 1075.93014); Commun. Math. Phys. 265, No. 3, 673--697 (2006; Zbl 1105.93008)], and of \textit{A. Shirikyan} [Commun. Math. Phys. 266, No. 1, 123--151 (2006; Zbl 1105.93016)], we prove that the system of second-grade fluids is approximately controllable by a finite-dimensional control force.Comment on: ``Entropy generation in nanofluid flow of Walters-B fluid with homogeneous-heterogeneous reactions''https://www.zbmath.org/1475.352862022-01-14T13:23:02.489162Z"Pantokratoras, Asterios"https://www.zbmath.org/authors/?q=ai:pantokratoras.asteriosComment on the paper [\textit{S. Qayyum} et al., ibid. 43, No. 9, 5657--5672 (2020; Zbl 1454.35298)].Interpretation of entropy generation in Williamson fluid flow with nonlinear thermal radiation and first-order velocity sliphttps://www.zbmath.org/1475.352872022-01-14T13:23:02.489162Z"Qayyum, Sumaira"https://www.zbmath.org/authors/?q=ai:qayyum.sumaira"Khan, M. Ijaz"https://www.zbmath.org/authors/?q=ai:khan.m-ijaz"Masood, Faria"https://www.zbmath.org/authors/?q=ai:masood.faria"Chu, Yu-Ming"https://www.zbmath.org/authors/?q=ai:chu.yuming"Kadry, Seifedine"https://www.zbmath.org/authors/?q=ai:kadry.seifedine"Nazeer, Mubbashar"https://www.zbmath.org/authors/?q=ai:nazeer.mubbasharSummary: This research article investigates the impacts of magnetohydrodynamics (MHD), nonlinear thermal radiation, Darcy-Forchheimer porous medium, viscous dissipation, first-order velocity slip, and convective boundary condition on the entropy generation optimization in flow of non-Newtonian fluid (Williamson fluid) towards a flat and stretchable surface. A general entropy equation is derived for thermal heat irreversibility, porosity irreversibility, Joule heating irreversibility, and fluid friction irreversibility. The bvp4c (built-in-shooting) technique is utilized to solve the governing equations for the entropy generation. Our obtained results highlight that enhancement in the thermal radiation and magnetic causes an abrupt change in the entropy generation rate. Moreover, the heat transfer rate and velocity gradient (skin friction) are calculated numerically subject to pertinent parameter, and the results are displayed in tabular form.The asymptotic behavior as \(t\to\infty\) of solution of the problem describing small fluctuations of stratified fluid in the rotating system of coordinateshttps://www.zbmath.org/1475.352882022-01-14T13:23:02.489162Z"Sviridova, Elena N."https://www.zbmath.org/authors/?q=ai:sviridova.elena-nSummary: This article is devoted to studying an initial-boundary value problem describing the small fluctuations of the exponentially stratified fluid in the rotating Cartesian system of coordinates. The fluid is stratified along the axis \(Ox_3\) coinciding with the axis of rotation: \(\rho_0(x_3)=A\exp(-2\beta x_3)\), where \(\beta>0\) is a parameter of stratification. The existence of solution is proved in Sobolev's spaces of integrated functions. Two terms of asymptotics of components of the solution are constructed.The asymptotic behavior as \(t\to\infty\) of the components of solution of the problem describing small fluctuations of stratified fluid rotation in the semi-space. I.https://www.zbmath.org/1475.352892022-01-14T13:23:02.489162Z"Sviridova, E. N."https://www.zbmath.org/authors/?q=ai:sviridova.elena-nSummary: This article is devoted to studying a number of components of solution of the system of partial differential equations. The system of equations describes the small fluctuations of the exponentially stratified and uniformly rotating fluid in the Cartesian system of coordinates \((x_1,x_2,x_3)\) rigidly connected with the rotating fluid. The fluid is stratified along the axis \(Ox_3\) coinciding with the axis of rotation: \(\rho_0(x_3)=A\exp(-2\beta x_3)\), where \(\beta>0\) is a parameter of stratification. The asymptotics of one of the components of the solution is constructed.Global well-posedness of the full compressible Hall-MHD equationshttps://www.zbmath.org/1475.352902022-01-14T13:23:02.489162Z"Tao, Qiang"https://www.zbmath.org/authors/?q=ai:tao.qiang"Zhu, Canze"https://www.zbmath.org/authors/?q=ai:zhu.canzeSummary: This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.Decay estimates of solutions to the compressible micropolar fluids system in \(\mathbb{R}^3\)https://www.zbmath.org/1475.352912022-01-14T13:23:02.489162Z"Tong, Leilei"https://www.zbmath.org/authors/?q=ai:tong.leilei"Pan, Ronghua"https://www.zbmath.org/authors/?q=ai:pan.ronghua"Tan, Zhong"https://www.zbmath.org/authors/?q=ai:tan.zhongSummary: This work is concerned with the compressible micropolar fluids system in three-dimensional space. We consider the asymptotic behavior of the solution to the Cauchy problem near the constant equilibrium state provided that the initial perturbation is sufficiently small. Under some assumptions of the initial data, we show that the solution of the Cauchy problem converges to its constant equilibrium state at the exact same \(L^2\)-decay rates as the linearized equations, which shows the convergence rates are optimal. The proof is based on the spectral analysis of the semigroup generated by the linearized equations and the nonlinear energy estimates.Global existence and large time behavior of classical solutions to the two-dimensional micropolar equations with large initial data and vacuumhttps://www.zbmath.org/1475.352932022-01-14T13:23:02.489162Z"Wan, Ling"https://www.zbmath.org/authors/?q=ai:wan.ling"Zhang, Lan"https://www.zbmath.org/authors/?q=ai:zhang.lanSummary: This paper concerns the global existence and large time behavior of classical, strong, and weak solutions to the two-dimensional compressible micropolar equations with large initial data and vacuum. We assume that the shear and angular viscosity coefficients are positive constants and the bulk coefficient is \(\lambda = \rho^{\beta} \), where \(\rho\) is the density and \(\beta > 3/2\). It is crucial to derive an upper bound of the density uniformly in the time such that all the classical, strong, and weak solutions converge to the equilibrium state as the time tends to infinity.Regularity and energy conservation for compressible isentropic magnetohydrodynamic equationshttps://www.zbmath.org/1475.352942022-01-14T13:23:02.489162Z"Wu, Zhonger"https://www.zbmath.org/authors/?q=ai:wu.zhonger"Tan, Zhong"https://www.zbmath.org/authors/?q=ai:tan.zhong|tan.zhong.1Summary: In this paper, we mainly study the local energy equation of the weak solutions of the compressible isentropic MHD equation defined on \(\mathbb{T}^3\). We prove that the regularity of the solution is sufficient to guarantee the balance of the total energy in the \(B_3^{\alpha , \infty}((0, T) \times \mathbb{T}^3)\) space. We adopt a variant of the method of \textit{E. Feireisl} et al. [Arch. Ration. Mech. Anal. 223, No. 3, 1375--1395 (2017; Zbl 1365.35113)].Global regularity of 2D temperature-dependent MHD-Boussinesq equations with zero thermal diffusivityhttps://www.zbmath.org/1475.352952022-01-14T13:23:02.489162Z"Ye, Zhuan"https://www.zbmath.org/authors/?q=ai:ye.zhuan.1|ye.zhuanSummary: This paper is concerned with a model of the two-dimensional zero thermal diffusivity magnetohydrodynamics-Boussinesq equations with the temperature-dependent viscosity and electrical conductivity. The main purpose of this paper is to establish the global regularity to this system with arbitrarily large initial data.The rigorous derivation of unipolar Euler-Maxwell system for electrons from bipolar Euler-Maxwell system by infinity-ion-mass limithttps://www.zbmath.org/1475.352962022-01-14T13:23:02.489162Z"Zhao, Liang"https://www.zbmath.org/authors/?q=ai:zhao.liang.3|zhao.liang.5|zhao.liang.2|zhao.liang|zhao.liang.4|zhao.liang.1Summary: In the paper, we consider the local-in-time and the global-in-time convergence of infinity-ion-mass limit for bipolar Euler-Maxwell systems by setting the mass of an electron \(m_e = 1\) and letting the mass of an ion \(m_i \rightarrow + \infty \). We use the method of asymptotic expansions to handle the local-in-time convergence problem and find that the limiting process from bipolar models to unipolar models is actually decoupling but not the vanishing of equations for the corresponding the other particle. Moreover, when the initial data are sufficiently close to the constant equilibrium state, we also establish the corresponding global-in-time convergence.The nonlinear Rayleigh-Stokes problem with Riemann-Liouville fractional derivativehttps://www.zbmath.org/1475.352972022-01-14T13:23:02.489162Z"Zhou, Yong"https://www.zbmath.org/authors/?q=ai:zhou.yong.1"Wang, Jing Na"https://www.zbmath.org/authors/?q=ai:wang.jing-naSummary: The Rayleigh-Stokes problem has gained much attention with the further study of non-Newtonain fluids. In this paper, we are interested in discussing the existence of solutions for nonlinear Rayleigh-Stokes problem for a generalized second grade fluid with Riemann-Liouville fractional derivative. We firstly show that the solution operator of the problem is compact and continuous in the uniform operator topology. Furtherly, we give an existence result of mild solutions for the nonlinear problem.An alpha-model of polymer solutions motionhttps://www.zbmath.org/1475.352982022-01-14T13:23:02.489162Z"Zvyagin, A. V."https://www.zbmath.org/authors/?q=ai:zvyagin.andrey-v|zvyagin.alexander-vSummary: In this paper, we study the initial-boundary value problem for an alpha-model, which describes the motion of weakly concentrated aqueous polymer solutions. We consider the mathematical model with a rheological relation, satisfying the objectivity principle. On the base of the topological approximation approach for studying hydrodynamic problems, we prove the existence of weak solutions to the alpha-model. We also demonstrate that solutions to the alpha-model converge to the solution of the original model as the value of the parameter alpha tends to zero.On a priori estimates of weak solutions of one nonhomogeneous problem of dynamics of viscoelastic medium with memoryhttps://www.zbmath.org/1475.352992022-01-14T13:23:02.489162Z"Zvyagin, V. G."https://www.zbmath.org/authors/?q=ai:zvyagin.viktor-grigorevich"Orlov, V. P."https://www.zbmath.org/authors/?q=ai:orlov.vladimir-pSummary: A priori estimates of weak solutions to a problem of dynamics of viscoelastic continuous medium with memory along trajectories of velocity field and nonhomogenous condition on the boundary is established.Strong solutions of one model of dynamics of thermoviscoelasticity of a continuous medium with memoryhttps://www.zbmath.org/1475.353002022-01-14T13:23:02.489162Z"Zvyagin, V. G."https://www.zbmath.org/authors/?q=ai:zvyagin.viktor-grigorevich"Orlov, V. P."https://www.zbmath.org/authors/?q=ai:orlov.vladimir-pSummary: We study a system of equations of dynamics of a thermoviscoelastic continuous medium with an Oldroyd-type rheological relation, which generalizes a Navier-Stokes-Fourier system. In the planar case, we prove the unique existence of strong solutions. The proof is based on the construction of Galerkin approximations and their strong estimates, which provide the corresponding limit passage.Existence of weak solutions to stationary and evolutionary Maxwell-Stokes type problems and the asymptotic behavior of the solutionhttps://www.zbmath.org/1475.353262022-01-14T13:23:02.489162Z"Aramaki, Junichi"https://www.zbmath.org/authors/?q=ai:aramaki.junichiSummary: We consider the existence of a weak solution to a class of evolutionary Maxwell-Stokes type problems containing a \(p\)-curlcurl system in a multiply-connected domainj. Moreover, we show that the weak solution converges to a weak solution of a stationary Maxwell-Stokes type problem as time tending to infinity.Magnetism and gravity. A unified treatmenthttps://www.zbmath.org/1475.353392022-01-14T13:23:02.489162Z"Alt, Hans Wilhelm"https://www.zbmath.org/authors/?q=ai:alt.hans-wilhelmSummary: In this paper we present a unified theory for gravitation and magnetization including electrodynamics. It is based on Maxwell's equations which in the form of Ampere's circuital law is the antisymmetric part of this theory, and the symmetric part is the gravity, which contains Newton's gravitation in the time-dependent relativistic version. Since magnetism and gravity are formulated in one system of differential equations, this new theory combines these two parts, and therefore this combination will probably bring some new insight to related problems which are discussed these days. \par We further study the related force in the mass-momentum system. This force consists of the well-known Newton force and the well-known Lorentz force. We show that they are exactly those forces that are predicted by our theory. We prove that these forces are equal to the divergence of a 4-flux in the mass-momentum equation. In this way these forces can be considered as internal expressions. In the proof all 4-fields of the new theory have to be 4-gradients of vector potentials, which is a well-known assumption.Mean field limit for Coulomb-type flowshttps://www.zbmath.org/1475.353412022-01-14T13:23:02.489162Z"Serfaty, Sylvia"https://www.zbmath.org/authors/?q=ai:serfaty.sylviaThe author establishes the mean field convergence for systems of points evolving along the gradient flow of their interaction energy when the interaction is the Coulomb potential or a super-Coulombic Riesz potential. This task is achieved in arbitrary dimensions, for the first time to the best of my knowledge.
The proof is based on a modulated energy method using a Coulomb or Riesz distance, assuming that the solutions of the limiting equation are regular enough. The method can handle the addition of a regular interaction kernel and applies also to conservative and mixed flows.
In the appendix, written together with Mitia Duerinckx, the mean field convergence is also proved for the solutions to Newton's law with Coulomb or Riesz interaction in the monokinetic case to solutions of an Euler-Poisson type system.
Reviewer: Dmitry Pelinovsky (Hamilton)Global classical solutions for the 2D four-component chemotaxis-Navier-Stokes equationshttps://www.zbmath.org/1475.353492022-01-14T13:23:02.489162Z"Du, Yaxin"https://www.zbmath.org/authors/?q=ai:du.yaxin"Zhang, Qian"https://www.zbmath.org/authors/?q=ai:zhang.qianSummary: In this paper, we consider a mathematical model describing the emergence of bioconvective patterns. Then we have a chemotaxis system with logistic source terms coupling with a Navier-Stokes equation. Using the Fourier localization technique and the regularity criterion, we establish the global classical solutions for the incompressible four-component chemotaxis-Navier-Stokes equations in \(\mathbb{R}^2\).A coupled PDE model of high intensity ultrasound heating of biological tissue. I: Well-posednesshttps://www.zbmath.org/1475.353502022-01-14T13:23:02.489162Z"Efendiev, M. A."https://www.zbmath.org/authors/?q=ai:efendiev.messoud"Murley, J."https://www.zbmath.org/authors/?q=ai:murley.jonathan"Sivaloganathan, S."https://www.zbmath.org/authors/?q=ai:sivaloganathan.sivabal|sivaloganathan.sivSummary: Over the past decade, High Intensity Focused Ultrasound (HIFU) has emerged as an important novel therapeutic modality in the treatment of cancers, that avoids many of the associated negative side effects of more well-established cancer therapies (eg chemotherapy and radiotherapy). In this paper, a coupled system of partial differential equations is used to model the interaction of HIFU with biological tissue. The mathematical model takes into account the effects of both diffusive and convective transport on the temperature field, when acoustic (ultrasound) energy is deposited at a particular location (focal point) in the biological tissue. The model poses significant challenges in establishing existence and uniqueness of solutions, which we consider to be a crucial first step in any realistic, applied mathematical study of HIFU therapy. In this paper, we establish well-posedncss of our model, using the Leray-Schauder principle, together with a-priori estimates.On the global well-posedness for the 3D axisymmetric incompressible Keller-Segel-Navier-Stokes equationshttps://www.zbmath.org/1475.353542022-01-14T13:23:02.489162Z"Hua, Qiang"https://www.zbmath.org/authors/?q=ai:hua.qiang"Zhang, Qian"https://www.zbmath.org/authors/?q=ai:zhang.qianThe authors consider a model of coral spawning which consists of the Keller-Segel chemotaxis system with a cubic reaction term coupled with the Navier-Stokes equations. Assuming symmetry properties of the fluid flow (axisymmetric, without swirl) they prove the global-in-time well-posedness of this system in suitable class of functions.
Reviewer: Piotr Biler (Wrocław)Existence of nonstationary Poiseuille-type solutions under minimal regularity assumptionshttps://www.zbmath.org/1475.353622022-01-14T13:23:02.489162Z"Pileckas, K."https://www.zbmath.org/authors/?q=ai:pileckas.konstantin"Čiegis, R."https://www.zbmath.org/authors/?q=ai:ciegis.raimondasSummary: Existence and uniqueness of a solution to the nonstationary Navier-Stokes equations having a prescribed flow rate (flux) in the infinite cylinder \(\Pi =\{x=(x^\prime , x_n)\in{{\mathbb{R}}}^n:\; x^\prime \in \sigma \subset{{\mathbb{R}}}^{n-1},\; -\infty<x_n<\infty ,\, n=2,3\}\) are proved. It is assumed that the flow rate \(F\in L^2(0, T)\) and the initial data \(\mathbf{u}_0=\big (0,\ldots ,0, u_{0n}\big )\in L^2(\sigma )\). The nonstationary Poiseuille solution has the form \(\mathbf{u}(x,t)=\big (0,\ldots ,0, U(x^\prime , t)\big ), \; p(x,t)=-q(t)x_n+p_0(t)\), where \((U(x',t), q(t))\) is a solution of an inverse problem for the heat equation with a specific over-determination condition.Increasing stability in acoustic and elastic inverse source problemshttps://www.zbmath.org/1475.354132022-01-14T13:23:02.489162Z"Entekhabi, Mozhgan"https://www.zbmath.org/authors/?q=ai:entekhabi.mozhgan-nora"Isakov, Victor"https://www.zbmath.org/authors/?q=ai:isakov.victorThe work is aimed to study increasing stability in the inverse scattering source problem for the Helmholtz equation and the classical Lamé system in the three dimensional space from boundary data at multiple wave numbers. As additional data for source identification the authors use pressure or displacement at the boundary of the reference domain which are natural and minimal data.
Applications include recovery of acoustic sources from boundary measurements of the pressure, in particular, detection of submarines and of material defects in various industrial objects. This type of inverse problem is also motivated by wide applications in biomedical imaging (magnetoencephalography), engineering, and geophysics, in particular, to locating sources of earthquakes.
Let \(u(x,k)\) solve the Helmholtz equation \((\Delta + k^2) u = -f\) in \(\mathbb{R}^3\) with real valued \(f \in H^0 (\mathbb{R}^3)\), \(\mathrm{supp} \ f \subset \Omega\); and satisfies the Sommerfeld radiation condition. The paper is aimed to investigate stability of recovery of \(f\) from the near field data, \(u = u_0\) on \(\partial \Omega\) when \(0 < k < K\). Here \(\Omega\) is a bounded domain in \(\mathbb{R}^3\) with the connected \(\mathbb{R}^3 \setminus \overline{\Omega}\) and the boundary \(\partial \Omega \in C^2\).
Next the authors consider the inverse scattering source problem for the elasticity system \((\mu \Delta + (\mu + \lambda)\nabla \mathrm{div} + \rho k^2) u = -\mathbf{f}\) in \(\mathbb{R}^3\) with the standard radiation condition. The authors consider the stability of recovery of \(\mathbf{f}\) from the near field data, \(u = u_0\) on \(\partial \Omega\) when \(0 < k < K\). Here \(\lambda\), \(\mu\) are constant Lamé parameters, real vector valued \(\mathbf{f} \in H^0(\mathbb{R}^3)\), \(\mathrm{supp} \ \mathbf{f} \subset \Omega\).
By using the Fourier transform with respect to the wave numbers, explicit bounds for analytic continuation, Huygens principle, sharp bounds for initial boundary value problems and increasing (with larger wave number intervals) stability estimates are obtained.
Reviewer: Elena V. Tabarintseva (Chelyabinsk)Well-posedness of the free boundary problem in elastodynamics with mixed stability conditionhttps://www.zbmath.org/1475.354242022-01-14T13:23:02.489162Z"Li, Hui"https://www.zbmath.org/authors/?q=ai:li.hui|li.hui.1|li.hui.5|li.hui.2|li.hui.4|li.hui.3"Wang, Wei"https://www.zbmath.org/authors/?q=ai:wang.wei.25|wang.wei.5|wang.wei.1|wang.wei.24|wang.wei.15|wang.wei.8|wang.wei.30|wang.wei.21|wang.wei.16|wang.wei.9|wang.wei.26|wang.wei.13|wang.wei.19|wang.wei.28|wang.wei.27|wang.wei.17|wang.wei.2|wang.wei.23|wang.wei.3|wang.wei.12|wang.wei.20|wang.wei.29"Zhang, Zhifei"https://www.zbmath.org/authors/?q=ai:zhang.zhifei.1|zhang.zhifeiThe authors prove a local solvability result for a free boundary problem arising in elastodynamics. The key ingredient is the derivation of a convenient relation for the velocity of the free boundary. Harmonic coordinates are used to reset the problem. The existence of local solutions (for the reformulated problem) is guaranteed by a compactness argument, while the uniqueness follows from a direct energy-type estimate.
Reviewer: Adrian Muntean (Karlstad)The shortest time and/or the shortest path strategies in a CA FF pedestrian dynamics modelhttps://www.zbmath.org/1475.370202022-01-14T13:23:02.489162Z"Kirik, Ekaterina S."https://www.zbmath.org/authors/?q=ai:kirik.ekaterina-s"Yurgel'yan, Tat'yana B."https://www.zbmath.org/authors/?q=ai:yurgelyan.tatyana-b"Krouglov, Dmitriy V."https://www.zbmath.org/authors/?q=ai:krouglov.dmitriy-vSummary: The paper deals with a mathematical model of a pedestrian movement based on a stochastic cellular automata (CA) approach. A basis of the model obtained is the Floor Field (FF) model. FF models imply that virtual people follow the shortest path strategy. However, in reality people follow the strategy of the shortest time as well. The focus of the paper is on mathematical formalization and implementation of these features into a model of pedestrian movement. Some results of computer simulations are presented.On discrete people movement model with environment analysishttps://www.zbmath.org/1475.370212022-01-14T13:23:02.489162Z"Kirik, Ekatherina S."https://www.zbmath.org/authors/?q=ai:kirik.ekatherina-s"Krouglov, Dmitriuı V."https://www.zbmath.org/authors/?q=ai:krouglov.dmitriui-v"Yurgel'yan, Tat'yana B."https://www.zbmath.org/authors/?q=ai:yurgelyan.tatyana-bSummary: A stochastic cellular automata (CA) model simulating pedestrian dynamics is presented. The obtained model simulates people movement from random style to directed. It provides an opportunity for pedestrian's environment analysis and realization of ``patient people'' strategy. A regular evacuation process is reproduced and investigated by means of the presented model.Finding extremal periodic orbits with polynomial optimization, with application to a nine-mode model of shear flowhttps://www.zbmath.org/1475.370942022-01-14T13:23:02.489162Z"Lakshmi, Mayur V."https://www.zbmath.org/authors/?q=ai:lakshmi.mayur-v"Fantuzzi, Giovanni"https://www.zbmath.org/authors/?q=ai:fantuzzi.giovanni"Fernández-Caballero, Jesús D."https://www.zbmath.org/authors/?q=ai:fernandez-caballero.jesus-d"Hwang, Yongyun"https://www.zbmath.org/authors/?q=ai:hwang.yongyun"Chernyshenko, Sergei I."https://www.zbmath.org/authors/?q=ai:chernyshenko.sergei-iIt has been long recognized the fundamental role played by unstable periodic orbits (UPOs) in the dynamics governed by nonlinear ordinary differential equations (ODEs). Thus, it is thought that they form the skeleton for the chaotic behavior exhibited by many systems. On the other hand, they constitute also the key point in techniques for control of chaos. It is thus very relevant to have as many tools as possible to compute UPOs in practice or at least to approximate them as accurately as possible.
The paper is devoted to the development of one such technique, specifically addressed to compute extremal UPOs, i.e., those that maximize or minimize the infinite-time average of a certain scalar function \(\Phi\), in ODEs with a polynomial vector field \(f\). The procedure is algorithmic and has two main steps:
(i) The construction of an auxiliary function \(V\) that produces a sharp as possible bound \(\lambda\) of the function \(\Phi\);
(ii) The numerical computation of the set of all points \(\mathcal{S}_{\varepsilon}\) where the function \(\lambda - \Phi - f \cdot \nabla V\) takes values not greater than some arbitrary \(\varepsilon > 0\).
It turns out that approximating extremal UPOs using the full set \(\mathcal{S}_{\varepsilon}\) for a given \(\varepsilon\) is a computationally intractable problem except for ODEs of very low dimension, and so some other heuristic approximation techniques have to be introduced in the previous process. As a result, there is no formal theoretical results guaranteeing that the procedure produces sufficiently accurate approximations to the sought orbit. Nevertheless, the practical application analyzed in the paper (a 9-dimensional quadratic ODE modeling a sinusoidally forced shear flow in a periodic channel) shows that the algorithm not only reproduces previous results concerning the existence of certain UPOs, but also provides evidence of new periodic trajectories in othes regimes of the Reynolds number.
The algorithm can be in principle applied to polynomial ODEs of arbitrary dimension and is amenable to several improvements both of minimization and the use of multiple-shooting techniques to determine the periodic orbit. It thus constitute a relevant step forward for the study of the dynamics of polynomial systems of ODEs.
Reviewer: Fernando Casas (Castellon)Optimal control of geometric partial differential equationshttps://www.zbmath.org/1475.490052022-01-14T13:23:02.489162Z"Hintermüller, Michael"https://www.zbmath.org/authors/?q=ai:hintermuller.michael"Keil, Tobias"https://www.zbmath.org/authors/?q=ai:keil.tobiasSummary: Optimal control problems for geometric (evolutionary) partial differential inclusions are considered. The focus is on problems which, in addition to the nonlinearity due to geometric evolution, contain optimization theoretic challenges because of non-smoothness. The latter might stem from energies containing non-smooth constituents such as obstacle-type potentials or terms modeling, e.g., pinning phenomena in microfluidics. Several techniques to remedy the resulting constraint degeneracy when deriving stationarity conditions are presented. A particular focus is on Yosida-type mollifications approximating the original degenerate problem by a sequence of non-degenerate nonconvex optimal control problems. This technique is also the starting point for the development of numerical solution schemes. In this context, also dual-weighted residual based error estimates are addressed to facilitate an adaptive mesh refinement. Concerning the underlying state model, sharp and diffuse interface formulations are discussed. While the former always allows for accurately tracing interfacial motion, the latter model may be dictated by the underlying physical phenomenon, where near the interface mixed phases may exist, but it may also be used as an approximate model for (sharp) interface motion. In view of the latter, (sharp interface) limits of diffuse interface models are addressed. For the sake of presentation, this exposition confines itself to phase field type diffuse interface models and, moreover, develops the optimal control of either of the two interface models along model applications. More precisely, electro-wetting on dielectric is used in the sharp interface context, and the control of multiphase fluids involving spinodal decomposition highlights the phase field technique. Mathematically, the former leads to a Hele-Shaw flow with geometric boundary conditions involving a complementarity system due to contact line pinning, and the latter gives rise to a Cahn-Hilliard Navier-Stokes model including a non-smooth obstacle type potential leading to a variational inequality constraint.
For the entire collection see [Zbl 1458.35003].Traffic congestion in expanders and \((p,\delta )\)-hyperbolic spaceshttps://www.zbmath.org/1475.530462022-01-14T13:23:02.489162Z"Li, Shi"https://www.zbmath.org/authors/?q=ai:li.shi"Tucci, Gabriel H."https://www.zbmath.org/authors/?q=ai:tucci.gabriel-hSummary: In this article we define the notion of \((p, \delta )\)-Gromov hyperbolic space where we relax the Gromov \textit{slimness} condition to allow that not all, but a positive fraction of all triangles, are \(\delta \)-slim. Furthermore, we study their traffic congestion under geodesic routing. We also construct a constant degree family of expanders with congestion \(\Theta (n^2)\) in contrast to random regular graphs that have congestion \(O(n \log^3(n))\).Well-posedness of SVI solutions to singular-degenerate stochastic porous media equations arising in self-organized criticalityhttps://www.zbmath.org/1475.601252022-01-14T13:23:02.489162Z"Neuss, Marius"https://www.zbmath.org/authors/?q=ai:neuss.mariusScaling of the steady-state load flow equations for multi-carrier energy systemshttps://www.zbmath.org/1475.650292022-01-14T13:23:02.489162Z"Markensteijn, A. S."https://www.zbmath.org/authors/?q=ai:markensteijn.a-s"Romate, J. E."https://www.zbmath.org/authors/?q=ai:romate.j-e"Vuik, C."https://www.zbmath.org/authors/?q=ai:vuik.cSummary: Coupling single-carrier networks (SCNs) into multi-carrier energy systems (MESs) has recently become more important. Steady-state load flow analysis of energy systems leads to a system of nonlinear equations, which is usually solved using the Newton-Raphson method (NR). Due to various physical scales within a SCN, and between different SCNs in a MES, scaling might be needed to solve the nonlinear system. In single-carrier electrical networks, per unit scaling is commonly used. However, in the gas and heat networks, various ways of scaling or no scaling are used. This paper presents a per unit system and matrix scaling for load flow models for a MES consisting of gas, electricity, and heat. The effect of scaling on NR is analyzed. A small example MES is used to demonstrate the two scaling methods. This paper shows that the per unit system and matrix scaling are equivalent, assuming infinite precision. In finite precision, the example shows that the NR iterations are slightly different for the two scaling methods. For this example, both scaling methods show the same convergence behavior of NR in finite precision.
For the entire collection see [Zbl 1471.65009].On a new spatial discretization for a regularized 3D compressible isothermal Navier-Stokes-Cahn-Hilliard system of equations with boundary conditionshttps://www.zbmath.org/1475.650632022-01-14T13:23:02.489162Z"Balashov, Vladislav"https://www.zbmath.org/authors/?q=ai:balashov.vladislav"Zlotnik, Alexander"https://www.zbmath.org/authors/?q=ai:zlotnik.alexander-aA novel spatial finite-difference discretization is constructed for a regularized 3D Navier-Stokes-Cahn-Hilliard system. Such a system describes flows of a viscous compressible isothermal two-component two-phase fluid with surface effects, where the potential body force is taken into consideration. In the discretization procedure, the main sought functions are defined on the same mesh, and an original approximation of the solid wall boundary conditions is proposed. This discretization has the total energy dissipativity property, which eliminates spurious currents. The discrete total mass and component mass conservation laws hold, and the discretization is also well-balanced for the equilibrium solutions. The non-convex part of the Helmholtz free energy is taken in a special logarithmic form, in order to guarantee that the concentration remains within a physically meaningful interval. The results of numerical 3D simulations are presented, together with a discussion on the role of the relaxation parameter.
Reviewer: Kanakadurga Sivakumar (Chennai)A lattice Boltzmann model for \((2+1)\)-dimensional solitary and periodic waves of the Calogero-Bogoyavlenskii-Schiff equationhttps://www.zbmath.org/1475.650832022-01-14T13:23:02.489162Z"Wang, Huimin"https://www.zbmath.org/authors/?q=ai:wang.huiminSummary: A lattice Boltzmann model is constructed to simulate the solitary and periodic wave solutions of the Calogero-Bogoyavlenskii-Schiff equation. Numerical simulations of the corresponding solitary and periodic waves show the efficiency of the method and a good computational accuracy.A posteriori subcell finite volume limiter for general \(P_NP_M\) schemes: applications from gasdynamics to relativistic magnetohydrodynamicshttps://www.zbmath.org/1475.650912022-01-14T13:23:02.489162Z"Gaburro, Elena"https://www.zbmath.org/authors/?q=ai:gaburro.elena"Dumbser, Michael"https://www.zbmath.org/authors/?q=ai:dumbser.michaelThe authors propose a new simple, robust, accurate and computationally efficient limiting strategy for the general family of ADER \(P_NP_M\) schemes, allowing the use of hybrid reconstructed methods (\(N > 0\), \(M > N\) ) in the modeling of discontinuous phenomena. This new approach has been applied to many different systems of hyperbolic conservation laws, providing highly accurate numerical results in all cases. The performance of the class of intermediate \(P_N P_M\) schemes with \(M > N > 0\) is compared with pure the Discontinuous Galerkin (DG) schemes (\(M = N\)). It is remarked that in the most cases the intermediate \(P_N P_M\) schemes lead to reduced computational cost compared with the pure DG methods. A new efficient posteriori subcell finite volume limiting strategy that is valid for the entire class of \(P_NP_M\) schemes is presented.
Reviewer: Abdallah Bradji (Annaba)High-order non-conservative simulation of hyperbolic moment models in partially-conservative formhttps://www.zbmath.org/1475.650932022-01-14T13:23:02.489162Z"Koellermeier, J."https://www.zbmath.org/authors/?q=ai:koellermeier.julian"Castro, M. J."https://www.zbmath.org/authors/?q=ai:castro.manuel-jSummary: In this paper the first dedicated study on high-order non-conservative numerical schemes for hyperbolic moment models is presented. The implementation uses a new formulation that allows for explicit evaluation of the model while satisfying conservation of mass, momentum, and energy. The high-order numerical schemes use a path-conservative treatment of the non-conservative terms and a new consistent evaluation of the eigenvalues. The numerical results of two initial value problems, one stationary test case and a boundary value problem, yield stable and accurate solutions with convergence towards the reference solution despite the presence of a non-conservative term. A large speedup or accuracy gain in comparison to existing first-order codes could be demonstrated.Computing ill-posed time-reversed 2D Navier-Stokes equations, using a stabilized explicit finite difference scheme marching backward in timehttps://www.zbmath.org/1475.651022022-01-14T13:23:02.489162Z"Carasso, Alfred S."https://www.zbmath.org/authors/?q=ai:carasso.alfred-sSummary: This paper constructs an unconditionally stable explicit finite difference scheme, marching backward in time, that can solve an interesting but limited class of ill-posed, time-reversed, 2D incompressible Navier-Stokes initial value problems. Stability is achieved by applying a compensating smoothing operator at each time step to quench the instability. This leads to a distortion away from the true solution. However, in many interesting cases, the cumulative error is sufficiently small to allow for useful results. Effective smoothing operators based on \((- \Delta)^p\), with real \(p>2\), can be efficiently synthesized using FFT algorithms. Similar stabilizing techniques were successfully applied in other ill-posed evolution equations. The analysis of numerical stability is restricted to a related linear problem. However, extensive numerical experiments indicate that such linear stability results remain valid when the explicit scheme is applied to a significant class of time-reversed nonlinear 2D Navier-Stokes initial value problems. Several reconstruction examples are included, based on the \textit{stream function-vorticity} formulation, and focusing on \(256 \times 256\) pixel images of recognizable objects. Such images, associated with non-smooth underlying intensity data, are used to create severely distorted data at time \(T>0\). Successful backward recovery is shown to be possible at parameter values exceeding expectations.Adaptive time stepping methods within a data assimilation framework applied to non-isothermal flow dynamicshttps://www.zbmath.org/1475.651152022-01-14T13:23:02.489162Z"Evert Uilhoorn, Ferdinand"https://www.zbmath.org/authors/?q=ai:uilhoorn.ferdinand-evertSummary: This contribution discusses the performance of time stepping schemes within a data assimilation framework, applied to the method of lines solutions of the non-isothermal compressible gas flow equations. We consider important classes of schemes, namely an embedded explicit Runge-Kutta (ERK) scheme, a diagonally implicit Runge-Kutta (DIRK) scheme, a fully implicit Runge-Kutta (IRK) scheme and a Rosenbrock-Krylov (ROK) scheme. For the numerical illustration, we estimated the flow transients in a subsea pipeline system. Errors from numerical discretization, missing and variability of physical parameters and inaccuracy of initial and boundary conditions are assumed non-Gaussian. Efficiency, robustness and estimation accuracy were evaluated. Results showed that the DIRK scheme is a good compromise between efficiency and robustness. Spurious oscillations were filtered out by the sequential Monte-Carlo algorithm.
For the entire collection see [Zbl 1471.65009].Enriched Galerkin method for the shallow-water equationshttps://www.zbmath.org/1475.651222022-01-14T13:23:02.489162Z"Hauck, Moritz"https://www.zbmath.org/authors/?q=ai:hauck.moritz"Aizinger, Vadym"https://www.zbmath.org/authors/?q=ai:aizinger.vadym"Frank, Florian"https://www.zbmath.org/authors/?q=ai:frank.florian"Hajduk, Hennes"https://www.zbmath.org/authors/?q=ai:hajduk.hennes"Rupp, Andreas"https://www.zbmath.org/authors/?q=ai:rupp.andreasIn this paper, the authors have considered the two-dimensional (2D) shallow-water equations. First, they have introduced the enriched Galerkin method for the system of 2D shallow-water equations. Then, they have shown the accuracy and robustness of the proposed method using an analytical convergence test. Finally, they have compared the enriched Galerkin method and discontinuous Galerkin method in terms of accuracy, stability, and robustness using artificial and realistic test problems.
Reviewer: J. Manimaran (Ponda)Approximate deconvolution with correction: a member of a new class of models for high Reynolds number flowshttps://www.zbmath.org/1475.651262022-01-14T13:23:02.489162Z"Labovsky, Alexander E."https://www.zbmath.org/authors/?q=ai:labovsky.alexander-eThis paper introduces a two-step defect correction method to the modeling of the high-Reynolds number flows, which combines the defect correction approach and the turbulence modeling. The method is investigated numerically and theoretically based on the approximate deconvolution models. The competitive performance of the method is shown on several benchmark problems, including a benchmark problem of finding maximal drag and lift coefficients, flow past the step, and the discussion on Taylor-Green vortex solutions.
Reviewer: Zhiming Chen (Beijing)Lagrange nodal discontinuous Galerkin method for fractional Navier-Stokes equationshttps://www.zbmath.org/1475.651382022-01-14T13:23:02.489162Z"Zhao, Jingjun"https://www.zbmath.org/authors/?q=ai:zhao.jingjun"Zhao, Wenjiao"https://www.zbmath.org/authors/?q=ai:zhao.wenjiao"Xu, Yang"https://www.zbmath.org/authors/?q=ai:xu.yang.1Summary: This paper provides a Lagrange nodal discontinuous Galerkin method for solving the time-dependent incompressible space fractional Navier-Stokes equations numerically. The existence and uniqueness of weak solutions are obtained. By combining the Lagrange method in temporal discretization and the hybridized discontinuous Galerkin method in spatial direction, the fully discrete scheme is presented and the stability is proved rigorously. Furthermore, the error estimates for the \(L^2\)-norm are derived in both the velocity and the pressure. Finally, some numerical experiments are given to illustrate the performance of the proposed method and validate the theoretical result.Numerical simulations for the quasi-3D fluid streamer propagation model: methods and applicationshttps://www.zbmath.org/1475.651392022-01-14T13:23:02.489162Z"Zhuang, Chijie"https://www.zbmath.org/authors/?q=ai:zhuang.chijie"Huang, Mengmin"https://www.zbmath.org/authors/?q=ai:huang.mengmin"Zeng, Rong"https://www.zbmath.org/authors/?q=ai:zeng.rongSummary: In this work, we propose and compare four different strategies for simulating the fluid model of quasi-three-dimensional streamer propagation, consisting of Poisson's equation for the particle velocity and two continuity equations for particle transport in the cylindrical coordinate system with angular symmetry. Each strategy involves one method for solving Poisson's equation, a discontinuous Galerkin method for solving the continuity equations, and a total variation-diminishing Runge-Kutta method in temporal discretization. The numerical methods for Poisson's equation include discontinuous Galerkin methods, the mixed finite element method, and the least-squares finite element method. The numerical method for continuity equations is the Oden-Babuška-Baumann discontinuous Galerkin method. A slope limiter for the DG methods in the cylindrical coordinate system is proposed to conserve the physical property. Tests and comparisons show that all four strategies are compatible in the sense that solutions to particle densities converge. Finally, different types of streamer propagation phenomena were simulated using the proposed method, including double-headed streamer in nitrogen and \(\mathrm{SF}_6\) between parallel plates, a streamer discharge in a point-to-plane gap.On entropy-stable discretizations and the entropy adjointhttps://www.zbmath.org/1475.651442022-01-14T13:23:02.489162Z"Hicken, Jason E."https://www.zbmath.org/authors/?q=ai:hicken.jason-eFor symmetrizable conservation laws, the entropy variables are adjoints for a functional that balances entropy flux into the domain with sources of entropy inside the domain. In this paper, it was shown that entropy-stable summation by parts (SBP) discretizations mimic an additional property of the continuous equations: the entropy adjoint. The entropy variables satisfy the discrete adjoint equation for a discretized entropy-balance functional if they are evaluated from the discrete solution. They are identical to the discrete adjoint variables up to machine accuracy. The theoretical results are verified for steady inviscid (Euler equation) and viscous flows (Navier-Stokes equation) over an airfoil.
Reviewer: Bülent Karasözen (Ankara)An efficient second order stabilized scheme for the two dimensional time fractional Allen-Cahn equationhttps://www.zbmath.org/1475.651452022-01-14T13:23:02.489162Z"Jia, Junqing"https://www.zbmath.org/authors/?q=ai:jia.junqing"Zhang, Hui"https://www.zbmath.org/authors/?q=ai:zhang.hui.1|zhang.hui.8|zhang.hui.3|zhang.hui|zhang.hui.7|zhang.hui.11|zhang.hui.2|zhang.hui.10|zhang.hui.4|zhang.hui.5|zhang.hui.6|zhang.hui.9"Xu, Huanying"https://www.zbmath.org/authors/?q=ai:xu.huanying"Jiang, Xiaoyun"https://www.zbmath.org/authors/?q=ai:jiang.xiaoyunSummary: In this paper, we give a stabilized second order scheme for the time fractional Allen-Cahn equation. The scheme uses the fractional backward difference formula (FBDF) for the time fractional derivative and the Legendre spectral method for the space approximation. The nonlinear terms are treated implicitly with a second order stabilized term. Based on the fractional Grönwall inequality, we strictly prove that the proposed scheme converges to second order accuracy in time and spectral accuracy in space. To save computation time and storage, a fast evaluation is developed. Finally, we give some numerical examples to show the configurations of phase field evolution and verify the effectiveness of the proposed methods.A parallel, non-spatial iterative, and rotational pressure projection method for the nonlinear fluid-fluid interactionhttps://www.zbmath.org/1475.651462022-01-14T13:23:02.489162Z"Li, Jian"https://www.zbmath.org/authors/?q=ai:li.jian.1"Gao, Jiawei"https://www.zbmath.org/authors/?q=ai:gao.jiawei"Shu, Yu"https://www.zbmath.org/authors/?q=ai:shu.yuSummary: In this paper, a parallel, non-spatial iterative, and rotational pressure projection method for the coupled Navier-Stokes equations is proposed and developed. As for each Navier-Stokes equation, one elliptic equation and one Possion equation at each time step determine the values of the velocity and pressure, respectively. Moreover, we only need to solve four simple linear equations, and the computational time of the whole system is greatly reduced. The rotational pressure projection method achieves the same accuracy as the traditional decoupled fractional time-stepping method. Furthermore, we apply the presented method, the rotational pressure projection method and the linear decoupled fractional time-stepping method to the submarine mountain problem. Compared to the streamline diagrams of these three methods from two aspects of accuracy and CPU times, we obtain that the presented method has good parallelism and is the most efficient method, the rotational pressure projection method is more efficient than the traditional decoupled fractional time-stepping method. Finally, numerical results verify that our proposed method has the high efficiency.The introduction of the surfing scheme for shock capturing with high-stability and high-speed convergencehttps://www.zbmath.org/1475.651592022-01-14T13:23:02.489162Z"Mollaei, Mehdi"https://www.zbmath.org/authors/?q=ai:mollaei.mehdi"Malek Jafarian, Seyyed Majid"https://www.zbmath.org/authors/?q=ai:malek-jafarian.seyyed-majidSummary: In this paper, a novel shock capturing scheme with high stability and speed of solution is presented. The scheme divides the dependent variables into two parts, i.e. Surf and Surfer, like surfing sport. The Surf part is calculated by applying the concept of Sobolev gradient on the dependent variables. Furthermore, it has the least difference with these variables, along with the lowest discretization error and the same equation. Hence, it is expected that this part can be solved at high stability conditions and large time steps. In addition, the Surfer part is obtained from the difference between the Surf part and the dependent variables. Therefore, only the error-maker operators (for example, a discontinuity like a shock) are in this part and accordingly it has a local nature. Due to this feature, it can be solved with fewer points compared to the Surf part. Therefore, its equation is solved as quickly as Surf equation, despite its limited stability conditions. Finally, the summation of the Surf and Surfer solutions makes the main solution. The scheme has been applied to the inviscid Burgers' equation with an initial value of the step function, and one-dimensional inviscid Euler flow through a nozzle with a shock wave. The stability condition for the Burgers' equation has been increased to a Courant number of \(10^{10}\) and the solution time for the Euler flow case has been decreased by one-fifth. Comparison of the results with traditional methods indicates the ultra-high stability and ultra-speed convergence of this scheme.Multistage preconditioning for adaptive discretization of porous media two-phase flowhttps://www.zbmath.org/1475.651692022-01-14T13:23:02.489162Z"Kane, Birane"https://www.zbmath.org/authors/?q=ai:kane.biraneSummary: We present a constrained pressure residual (CPR) two-stage preconditioner applied to a discontinuous Galerkin discretization of a two-phase flow in strongly heterogeneous porous media. We consider a fully implicit, locally conservative, higher order discretization on adaptively generated meshes. The implementation is based on the open-source PDE software framework Dune and its PETSc binding.
For the entire collection see [Zbl 1471.65009].Wells' identification and transmissivity estimation in porous mediahttps://www.zbmath.org/1475.651732022-01-14T13:23:02.489162Z"Ameur, Hend Ben"https://www.zbmath.org/authors/?q=ai:ameur.hend-ben"Hariga-Tlatli, Nejla"https://www.zbmath.org/authors/?q=ai:tlatli.nejla-hariga"Mansouri, Wafa"https://www.zbmath.org/authors/?q=ai:mansouri.wafaSummary: This paper deals with the inverse problems of wells' location and transmissivity estimation in a saturated porous media. Wells are considered as circular holes and the heterogeneous domain is divided into zones with constant transmissivity in each one. The main used tool for wells' location is the topological gradient method applied to a design function defined with respect to available data. Moreover, this technique is incorporated in an adaptive parameterization algorithm leading, in a progressive way, to recover interfaces between hydrogeological zones and transmissivity values. The obtained algorithm allows to recover jointly the transmissivities and the wells' locations. Then the proposed method is tested on a simplified model inspired from the Rocky Mountain aquifer.Identification of obstacles immersed in a stationary Oseen fluid via boundary measurementshttps://www.zbmath.org/1475.651752022-01-14T13:23:02.489162Z"Karageorghis, Andreas"https://www.zbmath.org/authors/?q=ai:karageorghis.andreas"Lesnic, Daniel"https://www.zbmath.org/authors/?q=ai:lesnic.danielSummary: In this paper we consider the interior inverse problem of identifying a rigid boundary of an annular infinitely long cylinder within which there is a stationary Oseen viscous fluid, by measuring various quantities such as the fluid velocity, fluid traction (stress force) and/or the pressure gradient on portions of the outer accessible boundary of the annular geometry. The inverse problems are nonlinear with respect to the variable polar radius parameterizing the unknown star-shaped obstacle. Although for the type of boundary data that we are considering the obstacle can be uniquely identified based on the principle of analytic continuation, its reconstruction is still unstable with respect to small errors in the measured data. In order to deal with this instability, the nonlinear Tikhonov regularization is employed. Obstacles of various shapes are numerically reconstructed using the method of fundamental solutions for approximating the fluid velocity and pressure combined with the \(\mathrm{MATLAB}^{\copyright}\) toolbox routine lsqnonlin for minimizing the nonlinear Tikhonov's regularization functional subject to simple bounds on the variables.\(p\)- and \(hp\)-virtual elements for the Stokes problemhttps://www.zbmath.org/1475.651872022-01-14T13:23:02.489162Z"Chernov, A."https://www.zbmath.org/authors/?q=ai:chernov.alexey"Marcati, C."https://www.zbmath.org/authors/?q=ai:marcati.carlo"Mascotto, L."https://www.zbmath.org/authors/?q=ai:mascotto.lorenzoThis article discusses the \(p\)- and \(hp\)-versions of the virtual element method for the Stokes problem on polygonal domains. The approach relies on the use of the one-to-one mapping between the Poisson-like and Stokes-like virtual element spaces for the velocities. The authors obtain an exponential rate of convergence for the \(hp\)-virtual element method and algebraic and exponential convergence rate of the \(p\)-version of the method.
Reviewer: Marius Ghergu (Dublin)A posteriori analysis of the Newton method applied to the Navier-Stokes problemhttps://www.zbmath.org/1475.651882022-01-14T13:23:02.489162Z"Dakroub, Jad"https://www.zbmath.org/authors/?q=ai:dakroub.jad"Faddoul, Joanna"https://www.zbmath.org/authors/?q=ai:faddoul.joanna"Sayah, Toni"https://www.zbmath.org/authors/?q=ai:sayah.toniSummary: In this paper we study the a posteriori error estimates for the Navier-Stokes equations. The problem is discretized using the finite element method and solved using the Newton iterative algorithm. A posteriori error estimate has been established based on two types of error indicators. Finally, numerical experiments and comparisons with previous works validate the proposed scheme and show the effectiveness of the studied algorithm.Stochastic Galerkin approximation of the Reynolds equation with irregular film thicknesshttps://www.zbmath.org/1475.651902022-01-14T13:23:02.489162Z"Gustafsson, Tom"https://www.zbmath.org/authors/?q=ai:gustafsson.tom"Hakula, Harri"https://www.zbmath.org/authors/?q=ai:hakula.harri"Leinonen, Matti"https://www.zbmath.org/authors/?q=ai:leinonen.mattiSummary: We consider the approximation of the Reynolds equation with an uncertain film thickness. The resulting stochastic partial differential equation is solved numerically by the stochastic Galerkin finite element method with high-order discretizations both in spatial and stochastic domains. We compute the pressure field of a journal bearing in various numerical examples that demonstrate the effectiveness and versatility of the approach. The results suggest that the stochastic Galerkin method is capable of supporting design when manufacturing imperfections are the main sources of uncertainty.Parameter robust preconditioning for multi-compartmental Darcy equationshttps://www.zbmath.org/1475.652002022-01-14T13:23:02.489162Z"Piersanti, Eleonora"https://www.zbmath.org/authors/?q=ai:piersanti.eleonora"Rognes, Marie E."https://www.zbmath.org/authors/?q=ai:rognes.marie-e"Mardal, Kent-Andre"https://www.zbmath.org/authors/?q=ai:mardal.kent-andreSummary: In this paper, we propose a new finite element solution approach to the multi-compartmental Darcy equations describing flow and interactions in a porous medium with multiple fluid compartments. We introduce a new numerical formulation and a block-diagonal preconditioner. The robustness with respect to variations in material parameters is demonstrated by theoretical considerations and numerical examples.
For the entire collection see [Zbl 1471.65009].A weak Galerkin finite element method for \(p\)-Laplacian problemhttps://www.zbmath.org/1475.652062022-01-14T13:23:02.489162Z"Ye, Xiu"https://www.zbmath.org/authors/?q=ai:ye.xiu"Zhang, Shangyou"https://www.zbmath.org/authors/?q=ai:zhang.shangyouSummary: In this paper, we introduce a weak Galerkin (WG) finite element method for \(p\)-Laplacian problem on general polytopal mesh. The quasi-optimal error estimates of the weak Galerkin finite element approximation are obtained. The numerical examples confirm the theory.Boundary element methods for acoustic scattering by fractal screenshttps://www.zbmath.org/1475.652092022-01-14T13:23:02.489162Z"Chandler-Wilde, Simon N."https://www.zbmath.org/authors/?q=ai:chandler-wilde.simon-n"Hewett, David P."https://www.zbmath.org/authors/?q=ai:hewett.david-p"Moiola, Andrea"https://www.zbmath.org/authors/?q=ai:moiola.andrea"Besson, Jeanne"https://www.zbmath.org/authors/?q=ai:besson.jeanneBoundary element methods (BEM) for scattering problems by fractal screens are studied in this article.
The main idea is to approximate the fractal screen by a sequence of smoother screens (prefractals) where well-posedness of the corresponding boundary integral equations is known and, consequently, classical methods like Galerkin BEM can be used for the discretization. Two types of fractal screens are considered: (i) sets with fractal boundaries and (ii) compact fractal sets with empty interior.
The (numerical) analysis of boundary integral equations on fractal sets requires various non-standard results (e.g., Sobolev spaces defined on screens) which are given in Sections 2--3.
Convergence results for sound-soft screen problems are found in Sections 4--5. The case where the fractal screen is a fixed point of an iterative function system is studied in detail. The main results are Theorem 5.2 and Theorem 5.3 where convergence of the Galerkin BEM is proven for the two types (i), (ii).
Section 6 contains various examples of screens, namely, Cantor sets in 2D and 3D, the Sierpinski triangle and snowflakes. Numerical experiments for these examples are found in Section 7.
Reviewer: Thomas Führer (Santiago)Multilevel optimized Schwarz methodshttps://www.zbmath.org/1475.652122022-01-14T13:23:02.489162Z"Gander, Martin J."https://www.zbmath.org/authors/?q=ai:gander.martin-j"Vanzan, Tommaso"https://www.zbmath.org/authors/?q=ai:vanzan.tommasoThis paper defines a two-level optimized Schwarz method (OSM) for elliptic partial differential equations, which solves the coarse space problem on a coarse mesh. A local mode convergence analysis is given both for overlapping and nonoverlapping decompositions, which also suggests how to choose the optimized transmission conditions. The two-level method is extended to a multilevel OSM which uses OSMs as smoothers on each level. The paper provides extensive numerical experiments for solving the advection diffusion equation, Helmholtz equation with a dispersion correction, and Stokes-Darcy coupling to illustrate the robustness of the proposed multilevel OSMs.
Reviewer: Zhiming Chen (Beijing)Morse index and stability of the planar \(N\)-vortex problemhttps://www.zbmath.org/1475.700172022-01-14T13:23:02.489162Z"Hu, Xijun"https://www.zbmath.org/authors/?q=ai:hu.xijun"Portaluri, Alessandro"https://www.zbmath.org/authors/?q=ai:portaluri.alessandro"Xing, Qin"https://www.zbmath.org/authors/?q=ai:xing.qinSummary: This paper concerns the investigation of the stability properties of relative equilibria which are rigidly rotating vortex configurations sometimes called vortex crystals, in the N-vortex problem. Such a configurations can be characterized as critical point of the Hamiltonian function restricted on the constant angular impulse hyper-surface in the phase space (topologically a pseudo-sphere whose coefficients are the circulation strengths of the vortices). Relative equilibria are generated by the circle action on the so-called shape pseudo-sphere (which generalize the standard shape sphere appearing in the study of the \(N\)-body problem). Inspired by the planar \(N\)-body problem, and after a geometrical and dynamical discussion of the problem, we investigate the relation intertwining the stability of relative equilibria and the inertia indices of the central configurations generating such equilibria. In the last section we applied our main results to some symmetric three and four vortices relative equilibria.Dynamics of fluid conveying pipes using Rayleigh theory under non-classical boundary conditionshttps://www.zbmath.org/1475.740492022-01-14T13:23:02.489162Z"Dagli, Begum Yurdanur"https://www.zbmath.org/authors/?q=ai:dagli.begum-yurdanur"Ergut, Abdulkerim"https://www.zbmath.org/authors/?q=ai:ergut.abdulkerimSummary: The dynamic behavior of fluid conveying pipe has been investigated by using Rayleigh theory to present the effect of non-classical boundary conditions on natural frequencies. The assumption of ideal fluid is used for acquiring the equation of motion for a uniform Rayleigh pipe. The ideal fluid moves in the vertical direction with pipe and the pipe makes small oscillations by Hamilton's variation principle. Euler equation is adopted for the modeling of the flow behavior in the pipe. Accordingly, the dimensionless partial differential equations of motion are converted into matrix equations and solved for two different set of non-classical boundary conditions. The natural frequencies are obtained depending on fluid velocity and stiffnesses of boundary conditions by using Rayleigh theory. The effect of mass ratio and slenderness ratio on vibration frequency is examined for the first three modes. The one-way FSI (fluid-structure interaction) technique is used by ANSYS software to determine natural frequencies of pipe. The results of first natural frequency based on the numerical solution performed by using ANSYS-FSI are compared with the results of analytical solution for Rayleigh pipe.Size-dependent vibration analysis of an axially moving sandwich beam with MR core and axially FGM faces layers in yawed supersonic airflowhttps://www.zbmath.org/1475.740502022-01-14T13:23:02.489162Z"Ghorbanpour Arani, A."https://www.zbmath.org/authors/?q=ai:ghorbanpour-arani.ali|ghorbanpour-arani.a-h"Soleymani, T."https://www.zbmath.org/authors/?q=ai:soleymani.tSummary: The aim of this article is to study the influences of aerodynamic pressure and axially moving behavior on the size-dependent vibration of a sandwich structure. Here, the core of sandwich structure is a magnetorheological (MR) fluid and face layers are made of functionally graded material (FGM). In order to obtain the aerodynamic pressure due to supersonic flow over upper face of structure, the linear piston theory is considered. The displacement field of sandwich structure is written according to layerwise theory and the size-dependent strain energy is obtained based on modified first strain gradient theory (MFSGT). The Hamilton's principle is applied to derive the governing equations of motion. In order to solve the partial differential equations, the Galerkin method is applied. To validate the presented formulation and solution method, the obtained results are compared with the available results in the literature, which shows a good agreement. The first set of results investigate the first five natural frequencies of MR sandwich beam based on the different MR materials. The variations of frequency and corresponding loss factor are plotted against aerodynamic pressure, length scale parameters, axially speed, intensity of external magnetic field, yaw angle, and power-law index, and the resulting trends in the plots are discussed in detail. Also, the parameters of critical aerodynamic pressure and critical axially speed in different conditions are tabulated.Aeroelastic stability analysis of a flexible panel subjected to an oblique shock based on an analytical modelhttps://www.zbmath.org/1475.740652022-01-14T13:23:02.489162Z"Ye, Liuqing"https://www.zbmath.org/authors/?q=ai:ye.liuqing"Ye, Zhengyin"https://www.zbmath.org/authors/?q=ai:ye.zhengyin"Ye, Kun"https://www.zbmath.org/authors/?q=ai:ye.kun"Wu, Jie"https://www.zbmath.org/authors/?q=ai:wu.jie.3|wu.jie.5|wu.jie.2|wu.jie.6|wu.jie.1|wu.jie.4|wu.jieSummary: For a deeper understanding of the physical phenomenology of shock-induced panel flutter, a theoretical model for analyzing aeroelastic stability of flexible panels subjected to an oblique shock has been developed. The von Kármán large deflection plate theory is used to account for the geometrical nonlinearity, and local first-order piston theory is employed to predict unsteady aerodynamic loading in shock-dominated flows. In order to consider the nonuniform static pressure differentials induced by the shock, we regard the final total displacement of the panel as the superposition of static deformation and dynamic displacement, which is in accord with the actual situation of physicality. The static deformation is obtained by solving the static aeroelastic equation, and then it is introduced into the dynamic aeroelastic equations in the form of the stiffness by the nonlinear induced loading. According to Lyapunov indirect method and the Routh-Hurwitz criterion, a theoretical solution for the aeroelastic stability boundaries of the flexible panel subjected to an oblique shock is derived. The results show that the presence of an impinging shock wave is found to produce panel flutter that is characteristically different from that with the shock-free condition. For a complex aeroelastic system in shock-dominated flows, there exists a game between the static pressure differential and the unsteady dynamic pressure. When the dynamic pressure gains the upper hand, the presence of shock reduces the aeroelastic stability of the panel. In contrast, when the static pressure difference has the upper hand, the presence of shock will enhance stability of the panel. The dimensionless aerodynamic parameter, which is the ratio of the non-dimensional static pressure to the non-dimensional dynamic pressure of the incoming flow, plays a significant role in aeroelastic stability of panels in shock-dominated flows. For different dimensionless aerodynamic parameters, the flutter boundaries will present different characteristics. As this dimensionless aerodynamic parameter increases, the non-dimensional critical flutter dynamic pressure will increase monotonously.Waves of different geometries in a porous medium saturated by a three-phase fluidhttps://www.zbmath.org/1475.740692022-01-14T13:23:02.489162Z"Sadovnikov, R. V."https://www.zbmath.org/authors/?q=ai:sadovnikov.r-vSummary: Waves of different geometries (plane, cylindrical and spherical) in a porous medium saturated by a three-phase fluid: water, oil and gas is considered. Unified dispersion relations for waves with different geometries are obtained. It is shown that the dependence of phase velocities on frequency is the same for plane, cylindrical and spherical waves (with axial symmetry) and independent of the geometry of the process.Acoustic radiation and transmission loss of FG-graphene composite plate under nonuniform edge loadinghttps://www.zbmath.org/1475.740712022-01-14T13:23:02.489162Z"Gunasekaran, Vijay"https://www.zbmath.org/authors/?q=ai:gunasekaran.vijay"Pitchaimani, Jeyaraj"https://www.zbmath.org/authors/?q=ai:pitchaimani.jeyaraj"Babu Mailan Chinnapandi, Lenin"https://www.zbmath.org/authors/?q=ai:babu-mailan-chinnapandi.leninSummary: The influence of nonuniform edge loads on the acoustic response of a functionally graded graphene reinforced composite plate is investigated analytically. The energy method is implemented to calculate the buckling load \((P_{cr})\). An analytical method based on Reddy's third-order shear deformation theorem is used to obtain the vibration response, and acoustic response is obtained using Rayleigh Integral. The nature of edge load variation on buckling and vibro-acoustic response is significant. Free vibration mode shape changes with an increase in edge load and consequently affects the resonant amplitude of responses also especially for the plates with a higher aspect ratio. Volume fraction and dispersion pattern of graphene nano-platelets also influences the resonance amplitudes. Plate with \(FG-GRC_C\) dispersion pattern has improved buckling and vibro-acoustic response behavior. Similarly, change in sound transmission loss level is significant in the stiffness region compared to the damping and mass dominated region.Propagation of elastic waves in saturated fluid porous mediumhttps://www.zbmath.org/1475.740742022-01-14T13:23:02.489162Z"Kukarskikh, L. A."https://www.zbmath.org/authors/?q=ai:kukarskikh.lyubov-a"Polenov, V. S."https://www.zbmath.org/authors/?q=ai:polenov.victor-sSummary: Based on the mathematical theory of explosions, shock waves are studied in a saturated porous chsrede liquid with viscosity of the liquid. It is shown that in such an environment, there are two types of longitudinal waves and one ransverse, and obtained the differential equations and their solutions to determine the intensity of the wave front. The example shows the effect of fluid viscosity and porosity on the propagation of spherical waves.An improved formulation for hybridizable discontinuous Galerkin fluid-structure interaction modeling with reduced computational expensehttps://www.zbmath.org/1475.741222022-01-14T13:23:02.489162Z"Sheldon, Jason P."https://www.zbmath.org/authors/?q=ai:sheldon.jason-p"Miller, Scott T."https://www.zbmath.org/authors/?q=ai:miller.scott-t"Pitt, Jonathan S."https://www.zbmath.org/authors/?q=ai:pitt.jonathan-sSummary: This work presents two computational efficiency improvements for the hybridizable discontinuous Galerkin (HDG) fluid-structure interaction (FSI) model presented by Sheldon et al. A new formulation for the solid is presented that eliminates the global displacement, resulting in the velocity being the only global solid variable. This necessitates a change to the solid-mesh displacement coupling, which is accounted for by coupling the local solid displacement to the global mesh displacement. Additionally, the mesh basis and test functions are restricted to linear polynomials, rather than being equal-order with the fluid and solid. This change increases the computational efficiency dynamically, with greater benefit the higher order the computation, when compared to an equal-order formulation. These two improvements result in a 50\% reduction in the number of global degrees of freedom for high-order simulations for both the fluid and solid domains, as well as an approximately 50\% reduction in the number of local fluid domain degrees of freedom for high-order simulations. The new, more efficient formulation is compared against that from Sheldon et al. and negligible change of accuracy is found.Incompressible fluid dynamicshttps://www.zbmath.org/1475.760012022-01-14T13:23:02.489162Z"Davidson, P. A."https://www.zbmath.org/authors/?q=ai:davidson.peter-alanPublisher's description: Incompressible Fluid Dynamics is a textbook for graduate and advanced undergraduate students of engineering, applied mathematics, and geophysics. The text comprises topics that establish the broad conceptual framework of the subject, expose key phenomena, and play an important role in the myriad of applications that exist in both nature and technology.
The first half of the book covers topics that include the inviscid equations of Euler and Bernoulli, the Navier-Stokes equation and some of its simpler exact solutions, laminar boundary layers and jets, potential flow theory with its various applications to aerodynamics, the theory of surface gravity waves, and flows with negligible inertia, such as suspensions, lubrication layers, and swimming micro-organisms.
The second half is more specialised. Vortex dynamics, which is so essential to many natural phenomena in fluid mechanics, is developed in detail. This is followed by chapters on stratified fluids and flows subject to a strong background rotation, both topics being central to our understanding of atmospheric and oceanic flows. Fluid instabilities and the transition to turbulence are also covered, followed by two chapters on fully developed turbulence.
The text is largely self-contained, and aims to combine mathematical precision with a breadth of engineering and geophysical applications. Throughout, physical insight is given priority over mathematical detail.Bio-mimetic swimmers in incompressible fluids. Modeling, well-posedness, and controllabilityhttps://www.zbmath.org/1475.760022022-01-14T13:23:02.489162Z"Khapalov, Alexander"https://www.zbmath.org/authors/?q=ai:khapalov.alexander-yuriPublisher's description: This monograph presents an original, concise mathematical theory for bio-mimetic swimmers in the framework of a coupled system of PDEs and ODEs. The authoritative research pioneered by the author serves as the basis for the method adopted here. This unique methodology consists of an original modelling approach, well-posedness results for the proposed models for swimmers, and a controllability theory that studies the steering potential of the proposed swimmers. A combination of this sort does not currently exist in the literature, making this an indispensable resource.
Structured in five parts, the author establishes the main modeling approach in Part One. Part Two then presents the well-posedness results for these models. Parts Three through Five serve to develop a controllability theory for the swimmers, which are conceived of as artificial mechanical devices that imitate the swimming motion of fish, eels, frogs, and other aquatic creatures in nature. Several illustrative examples are provided in the last portion that serve as potential research topics.
\textit{Bio-Mimetic Swimmers in Incompressible Fluids} will appeal to graduate students and researchers studying fluid dynamics and control theory, as well as engineers interested in these areas.Topological methods in hydrodynamicshttps://www.zbmath.org/1475.760032022-01-14T13:23:02.489162Z"Arnold, Vladimir I."https://www.zbmath.org/authors/?q=ai:arnold.vladimir-igorevich"Khesin, Boris A."https://www.zbmath.org/authors/?q=ai:khesin.boris-aPublisher's description: First published in 1998 this unique monograph treats topological, group-theoretic, and geometric problems of ideal hydrodynamics and magneto-hydrodynamics from a unified point of view.
It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. This book, now accepted as one of the main references in the field, is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry. The updated second edition also contains a survey of recent developments in this now-flourishing field of topological and geometric hydrodynamics.
See the review of the first edition in [Zbl 0902.76001].Mathematical theory of liquid interfaces. Liquid layers, capillary interfaces, floating drops and particleshttps://www.zbmath.org/1475.760042022-01-14T13:23:02.489162Z"Miersemann, Erich"https://www.zbmath.org/authors/?q=ai:miersemann.erichThis book is designed as to present a panoramic overview of the mathematical foundation of various aspects of liquid layers, capillary interfaces, floating drops and particles. As the author himself wrote, these considerations were suggested actually by the present day space technology and micro-mechanics where liquids are inevitably involved. The most trivial examples that one can point out are liquids under low or zero gravity, and liquids of small volume or liquids in small containers. The book is structured in ten chapters of which ``Capillary Interfaces'' (Chapter 3) and ``Asymptotic Formulas'' (Chapter 7) are the most voluminous with respectively 50 and 32 pages. More than 70 problems are scattered throughout the text, from which some are real exercises, while the rest are still open problems. It is very nice that the book is illustrated with more than 90 Figures and photographs which principal aim is to increase the understanding. Unfortunately, some of the figures were prepared carelessly -- the fonts of the symbols inside are different from those used in the text and not all of them are explained clearly on the page, while at some places they are simply missing. At other places different notation are used interchangeably (cf., e.g., p. 185) where \(\kappa_i, \kappa_e\) and \(\kappa i, \kappa e\) can be seen to denote the same things. The list of references however is quite representative with just one notable omission namely the book by \textit{J. McCuan} [The stability of cylindrical pendant drops. Providence, RI: American Mathematical Society (AMS) (2017; Zbl 1400.76003)].
Comparing them, one can notice that in the book by the author there are not many worked out to the very end examples, while in that one by McCuan one can find plenty of such. So, the reviewer's suggestion for the potential reader is that he/she should have both of these books on the shelve as they represent different (and in many cases complementary) styles of thinking.
Reviewer: Ivailo M. Mladenov (Sofia)Investigation of the solvability of one stationary model non-Newtonian fluid motion in unbounded domainhttps://www.zbmath.org/1475.760052022-01-14T13:23:02.489162Z"Zvyagin, A. V."https://www.zbmath.org/authors/?q=ai:zvyagin.alexander-v|zvyagin.andrey-vSummary: This paper establishes the solvability in weak sense for a model describing the stationary motion of weak aqueous polymer solutions in the unboundary domain with the objective derivative in the rheological relation.The slip flow of generalized Maxwell fluids with time-distributed characteristics in a rotating microchannelhttps://www.zbmath.org/1475.760062022-01-14T13:23:02.489162Z"Feng, Chenqing"https://www.zbmath.org/authors/?q=ai:feng.chenqing"Si, Xinhui"https://www.zbmath.org/authors/?q=ai:si.xinhui"Cao, Limei"https://www.zbmath.org/authors/?q=ai:cao.limei"Zhu, Beibei"https://www.zbmath.org/authors/?q=ai:zhu.beibeiSummary: A time-distributed order fractional continuity model is proposed to simulate the rotating electro-osmotic slip flow of generalized Maxwell fluids in an alternating electric field. The model fully exhibits the wider memory characteristics of viscoelastic fluid. Complex momentum equation is discretized by L1 and L2 algorithms and verified by constructing analytical solutions method. Due to the stronger memory of generalized Maxwell fluids, reverse flow is restrained, and the time for oscillation reaching the steady state is postponed. Moreover, with the increase of Debye-Hückle coefficient the velocity will increase rapidly.Strong apriori estimates of solutions to nonhomogeneous initial-boundary value problem for one model of viscoelastic mediumhttps://www.zbmath.org/1475.760072022-01-14T13:23:02.489162Z"Orlov, V. P."https://www.zbmath.org/authors/?q=ai:orlov.vladimir-pSummary: Second apriori estimate to solutions for some model of dynamics of viscoelastic continuous medium in the planar case are established.Simulating two-dimensional viscoelastic fluid flows by means of the ``tensor diffusion'' approachhttps://www.zbmath.org/1475.760082022-01-14T13:23:02.489162Z"Westervoß, Patrick"https://www.zbmath.org/authors/?q=ai:westervoss.patrick"Turek, Stefan"https://www.zbmath.org/authors/?q=ai:turek.stefanSummary: In this work, the novel ``Tensor Diffusion'' approach for simulating viscoelastic fluids is proposed, which is based on the idea, that the extra-stress tensor in the momentum equation of the flow model is replaced by a product of the strain-rate tensor and a tensor-valued viscosity. At least for simple flows, this approach offers the possibility to reduce the full nonlinear viscoelastic model to a generalized ``Tensor Stokes'' problem, avoiding the need of considering a separate stress tensor in the solution process. Besides fully developed channel flows, the ``Tensor Diffusion'' approach is evaluated as well in the context of general two-dimensional flow configurations, which are simulated by a suitable four-field formulation of the viscoelastic model respecting the ``Tensor Diffusion''.
For the entire collection see [Zbl 1471.65009].Information reduction for chaotic patternshttps://www.zbmath.org/1475.760092022-01-14T13:23:02.489162Z"Hidaka, Yoshiki"https://www.zbmath.org/authors/?q=ai:hidaka.yoshiki"Ijigawa, Kosuke"https://www.zbmath.org/authors/?q=ai:ijigawa.kosuke"Kwak, Seung-Yong"https://www.zbmath.org/authors/?q=ai:kwak.seung-yong"Oikawa, Noriko"https://www.zbmath.org/authors/?q=ai:oikawa.noriko"Okabe, Hirotaka"https://www.zbmath.org/authors/?q=ai:okabe.hirotaka"Hara, Kazuhiro"https://www.zbmath.org/authors/?q=ai:hara.kazuhiroSummary: To investigate the universality and diversity of spatiotemporal chaos, information reduction, which describes phenomena using generalized quantities such as amplitude and phase, is an important technique. Several methods of image analysis are presented for information reduction of experimental image data of spatiotemporal chaos.Stratification in drying films: a diffusion-diffusiophoresis modelhttps://www.zbmath.org/1475.760102022-01-14T13:23:02.489162Z"Rees-Zimmerman, Clare R."https://www.zbmath.org/authors/?q=ai:rees-zimmerman.clare-r"Routh, Alexander F."https://www.zbmath.org/authors/?q=ai:routh.alexander-fSummary: This research is motivated by the desire to control the solids distribution during the drying of a film containing particles of two different sizes. A variety of particle arrangements in dried films has been seen experimentally, including a thin layer of small particles at the top surface. However, it is not fully understood why this would occur. This work formulates and solves a colloidal hydrodynamics model for (i) diffusion alone and (ii) diffusion plus excluded volume diffusiophoresis, to determine their relative importance in affecting the particle arrangement. The methodology followed is to derive partial differential equations (PDEs) describing the motion of two components in a drying film. The diffusive fluxes are predicted by generalising the Stokes-Einstein diffusion coefficient, with the dispersion compressibility used to produce equations valid up until close packing. A further set of novel equations incorporating diffusiophoresis is derived. The diffusiophoretic mechanism investigated in this work is the small particles being excluded from a volume around the large particles. The resulting PDEs are scaled and solved numerically using a finite volume method. The model includes the chemical potentials of the particles, allowing for incorporation of any interaction term. The relative magnitudes of the fluxes of the differently sized particles are compared using scaling arguments and via numerical results. The diffusion results, without any inter-particle interactions, predict stratification of large particles to the top surface. Addition of excluded volume diffusiophoresis introduces a downwards flux on the large particles, that can result in small-on-top stratification, thus providing a potential explanation of the experimental observations.Thermal capillary wave growth and surface roughening of nanoscale liquid filmshttps://www.zbmath.org/1475.760112022-01-14T13:23:02.489162Z"Zhang, Y."https://www.zbmath.org/authors/?q=ai:zhang.yuqin|zhang.yaxuan|zhang.youyou|zhang.yuting|zhang.yanli|zhang.yuzhong|zhang.yuning|zhang.yilin|zhang.yuanxiang|zhang.yuanqiao|zhang.yuduo|zhang.yanan|zhang.yinghui|zhang.yuejie|zhang.yingyuan|zhang.yingzhi|zhang.yihua|zhang.yong.13|zhang.yufeng|zhang.yi.5|zhang.yingfang|zhang.youfeng|zhang.yiyi|zhang.yinhu|zhang.yiyue|zhang.yuhuan|zhang.yaqian|zhang.yaqing|zhang.yafang|zhang.yuezhe|zhang.yuanfan|zhang.yuanzhang|zhang.ying.3|zhang.yanlong|zhang.yudong|zhang.yongxia|zhang.yuheng|zhang.yameng|zhang.yaoting.1|zhang.yi-ci|zhang.yanyong|zhang.yongou|zhang.youqian|zhang.yongpeng|zhang.yunbo|zhang.yongxu|zhang.yong.5|zhang.yongchuan|zhang.yule|zhang.yan-qing|zhang.yuwen|zhang.yaoyun|zhang.yuehui|zhang.yining|zhang.youguang|zhang.yijin|zhang.yuanji.1|zhang.yuanzhong|zhang.yuzhao|zhang.ya|zhang.yingbi|zhang.yuhua|zhang.yuqing|zhang.yuchun|zhang.yuexin|zhang.yeping|zhang.yini|zhang.yanshuang|zhang.yingbo|zhang.yongping|zhang.yuhe|zhang.yingshi|zhang.yanlan|zhang.yuanju|zhang.ye|zhang.yaguang|zhang.yuke|zhang.yarui|zhang.yitong|zhang.yingnan.1|zhang.yiyang|zhang.yaxing|zhang.yanhuan|zhang.yukun|zhang.yingfan|zhang.yonghao|zhang.yingshan|zhang.yingman|zhang.yumeng|zhang.yiqi|zhang.yanpu|zhang.yandan|zhang.youping|zhang.yutian|zhang.yushan|zhang.yongcun|zhang.yi.10|zhang.yaojun|zhang.yangming|zhang.yahui|zhang.yingqing|zhang.yuanle|zhang.yunxin|zhang.yiyun|zhang.yibin|zhang.yanjing|zhang.yanshan|zhang.yiqing|zhang.yude|zhang.yiguang|zhang.yapu|zhang.yingjun|zhang.yaming|zhang.yanni|zhang.yubai|zhang.yacong|zhang.yanhui|zhang.yunmei|zhang.yinhe|zhang.yanzhou|zhang.yuan|zhang.yichen|zhang.yejiang|zhang.yunning|zhang.yidu|zhang.yamin|zhang.youbing|zhang.yuqiang|zhang.yingfeng|zhang.yunhuang|zhang.yuelan|zhang.yonghu|zhang.yaoyao|zhang.yishi|zhang.yongheng|zhang.yicai|zhang.yuyue|zhang.yikai|zhang.yongcang|zhang.yingwen|zhang.yanhu|zhang.yirui|zhang.yongjie|zhang.yunyong|zhang.yunpu|zhang.yingbin|zhang.yalin|zhang.yidian|zhang.yuying|zhang.yunfei|zhang.yaqin|zhang.yahong|zhang.yuezhu|zhang.yingli|zhang.yang|zhang.youhua|zhang.yimin|zhang.yingjie|zhang.youhui|zhang.yuzhen|zhang.yinying|zhang.yuanqi|zhang.yuecheng|zhang.yuncheng|zhang.yanguo|zhang.yifeng|zhang.yuwei|zhang.yingsong|zhang.yunzhou|zhang.yong.1|zhang.yige|zhang.youzheng|zhang.yueyang|zhang.yueyun|zhang.yinda|zhang.yanci|zhang.yingying.2|zhang.yiwen|zhang.yujun|zhang.yancheng|zhang.yixiao|zhang.yifei.1|zhang.yinglong|zhang.yunxia|zhang.yaoting|zhang.yongjin|zhang.yingxuan|zhang.yingmei|zhang.yijie|zhang.yao|zhang.yuqiong|zhang.yaoxian|zhang.yinping|zhang.yipeng|zhang.yixue|zhang.yingrong|zhang.yongshuo|zhang.yunkai|zhang.yousheng|zhang.yang.5|zhang.yuanjiao|zhang.yanhang|zhang.yifei|zhang.yongling|zhang.yongbing.1|zhang.yuhao|zhang.yinshuang|zhang.yiyu|zhang.youtang|zhang.yuze|zhang.yibo|zhang.yanru|zhang.yuanying|zhang.yilun|zhang.yating|zhang.yusi|zhang.yongqin|zhang.yanxin|zhang.yangsen|zhang.yupeng|zhang.yu-feng|zhang.yuewei|zhang.yunli|zhang.yi.8|zhang.yangjun|zhang.yansong|zhang.yongbing.2|zhang.yongwei|zhang.yucun|zhang.yuanfun|zhang.yajie|zhang.yun|zhang.yuzhuo|zhang.yisheng|zhang.yulong|zhang.yangang|zhang.yuankun|zhang.yinglu|zhang.yurui|zhang.yueping|zhang.yingqian|zhang.yihao|zhang.yakun|zhang.yuhai|zhang.yiying|zhang.youan|zhang.yungui|zhang.youling|zhang.yaoli|zhang.yimo|zhang.yixin|zhang.yang.3|zhang.yongqing|zhang.yingzhou|zhang.yonghong|zhang.yumei|zhang.yinhui|zhang.yajun|zhang.yongchao|zhang.yanpeng|zhang.yanting|zhang.yinchao|zhang.yifang|zhang.yunhe|zhang.yan.5|zhang.yinpeng|zhang.yongjun|zhang.yuanyi|zhang.yafei|zhang.ying.1|zhang.yucai|zhang.yashun|zhang.yunqin|zhang.youpu|zhang.yuxia|zhang.yanju|zhang.yurong|zhang.yiye|zhang.yuntao|zhang.yanxia|zhang.yuanhui|zhang.yaru|zhang.yuanzhao|zhang.yi.12|zhang.yi-mu|zhang.yongchang|zhang.yongkui|zhang.yinglin|zhang.yunxi|zhang.yanjun|zhang.yuren|zhang.yunguang|zhang.yaoxue|zhang.yingying.4|zhang.yaxiu|zhang.yinghua|zhang.yonghua|zhang.yang.6|zhang.yamiao|zhang.yaowen|zhang.yubo|zhang.yujia|zhang.yanbiao|zhang.yangjing|zhang.yichi|zhang.yongde|zhang.yougquan|zhang.yuankai|zhang.yajing|zhang.yinbo|zhang.yunxiao|zhang.yuezhi|zhang.yongqian|zhang.yihuang|zheng.yuliang|zhang.youlin|zhang.yali|zhang.yicheng|zhang.yidong|zhang.yanming|zhang.yachong|zhang.yongzhan|zhang.yingshu|zhang.yu.1|zhang.yutong|zhang.yong.11|zhang.yunjia|zhang.yingying|zhang.yanqiu|zhang.yueling|zhang.yujuan|zhang.yuanzheng|zhang.yi|zhang.yuanquan|zhang.yaxiao|zhang.yi.6|zhang.yuqian|zhang.yuesheng|zhang.yuanhang|zhang.yong.8|zhang.yiheng|zhang.yangwen|zhang.yingtao|zhang.yanling|zhang.youyun|zhang.yangyi|zhang.yayun|zhang.yuyu|zhang.yimeng|zhang.yanjie|zhang.yanliu|zhang.yangyang|zhang.yannan|zhang.yushen|zhang.yuliang|zhang.yusen|zhang.yu-feng.3|zhang.youcun|zhang.yonglai|zhang.yuanpeng|zhang.yazhuo|zhang.yaoyu|zhang.yuancao|zhang.yukong|zhang.yueming|zhang.yabing|zhang.yangwu|zhang.yihuai|zhang.yuanjiang|zhang.yahan|zhang.yizhen|zhang.yukang|zhang.yudi|zhang.yunxing|zhang.yuanshu|zhang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yiman|zhang.yingqiu|zhang.yixiang|zhang.yuanli|zhang.yixuan|zhang.yanzhi|zhang.yanchun|zhang.yongxiang|zhang.yujie|zhang.yunzhang|zhang.yuedong|zhang.ying-lan|zhang.yongbo|zhang.yingkui|zhang.yuquan|zhang.yashan|zhang.yueli|zhang.yiping|zhang.yongkang|zhang.yunjun|zhang.yezhi|zhang.yigong|zhang.yongchun|zhang.yuanfeng|zhang.yuchen.1|zhang.yuxiang|zhang.yuwang|zhang.yunyi|zhang.yong.14|zhang.yaozong|zhang.yongzheng|zhang.yuanshuai|zhang.yuchao|zhang.yanying|zhang.yichong|zhang.youjun|zhang.yuyang|zhang.yongxin|zhang.yane|zhang.yuanhao|zhang.yuanjie|zhang.yubing|zhang.yinkui|zhang.yingya|zhang.yuhang|zhang.yulu|zhang.yanqiang|zhang.yaocun|zhang.yongpo|zhang.yicai.1|zhang.yongfei|zhang.youjian|zhang.yanzhen|zhang.yongsheng.1|zhang.yuzhou|zhang.yida|zhang.yuanwen|zhang.yongzhen|zhang.yuanyan|zhang.yaping|zhang.yanliang|zhang.yinsheng|zhang.yaosheng|zhang.youmei|zhang.yongzhi|zhang.yongji|zhang.yunan|zhang.yong.9|zhang.yunong|zhang.yifu|zhang.yunshui|zhang.yongan|zhang.yimin.1|zhang.yueliang|zhang.yiran|zhang.yaozhong|zhang.yan.4|zhang.yuanyuan|zhang.yingjian|zhang.yingkai|zhang.ying|zhang.yufen|zhang.yong.2|zhang.yaohua|zhang.yiqiang|zhang.yiteng|zhang.yongzhong|zhang.yongtao|zhang.yinong|zhang.yaotian|zhang.yuanbiao|zhang.yuzhi|zhang.yanfang|zhang.yueyang.1|zhang.yongshen"Sprittles, J. E."https://www.zbmath.org/authors/?q=ai:sprittles.james-e"Lockerby, D. A."https://www.zbmath.org/authors/?q=ai:lockerby.duncan-aSummary: The well-known thermal capillary wave theory, which describes the capillary spectrum of the free surface of a liquid film, does not reveal the transient dynamics of surface waves, e.g. the process through which a smooth surface becomes rough. Here, a Langevin model is proposed that can capture this dynamics, goes beyond the long-wave paradigm which can be inaccurate at the nanoscale, and is validated using molecular dynamics simulations for nanoscale films on both planar and cylindrical substrates. We show that a scaling relation exists for surface roughening of a planar film and the scaling exponents belong to a specific universality class. The capillary spectra of planar films are found to advance towards a static spectrum, with the roughness of the surface \(W\) increasing as a power law of time \(W\sim t^{1/8}\) before saturation. However, the spectra of an annular film (with outer radius \(h_0\)) are unbounded for dimensionless wavenumber \(qh_0<1\) due to the Rayleigh-Plateau instability.Eigenfrequencies of the oscillating surface of a free-falling compound drop of an ideal liquidhttps://www.zbmath.org/1475.760122022-01-14T13:23:02.489162Z"Shiryaev, A. A."https://www.zbmath.org/authors/?q=ai:shiryaev.a-aSummary: The surface oscillations of a two-layer drop of an ideal liquid are analyzed. It is shown that two different oscillation frequencies of the taken mode can exist. The effect of the main parameters of the liquids that compose the drop on the mode oscillation eigenfrequencies is analyzed. It is found that a relative decrease in the outer liquid layer thickness leads to a decrease in the eigenfrequencies of both in-phase and out-of-phase oscillations. An increase in the difference between the surface tension coefficients leads to an increase in the eigenfrequencies. Relative increase in the inner liquid density increases the eigenfrequencies of the in-phase mode and affects only slightly the eigenfrequencies of the out-of-phase mode. Simplified expressions for the dependences of the eigenfrequencies of oscillating free surface of a compound drop on parameters are obtained.Flow around a circular cylindrical shellhttps://www.zbmath.org/1475.760132022-01-14T13:23:02.489162Z"Khakimov, A. G."https://www.zbmath.org/authors/?q=ai:khakimov.a-g.1Summary: The results of the simulation of separationless jet flow around an elastic cylindrical shell under nonlinear boundary conditions are presented. The mean pressure action on the shell is taken into account. The solution is obtained in the form of series in the powers of the aerohydroelasticity parameter. The shapes of the shell cross-section, the pressure distributions over the deformed and undeformed shell, the distribution of the dimensionless bending moment, and the shear and tension forces are presented.Fluid oscillations in cylindrical tanks with longitudinal damping partitionshttps://www.zbmath.org/1475.760142022-01-14T13:23:02.489162Z"Buzhinskii, V. A."https://www.zbmath.org/authors/?q=ai:buzhinskii.v-aSummary: An asymptotic method for investigating small oscillations of fluids in cylindrical tanks with longitudinal damping partitions is presented. The effect of the number and width of partitions on the hydrodynamic parameters and the damping coefficients of fluid oscillations is studied in detail for the case of a circular cylindrical enclosure with a plane bottom. The numerical results are obtained using the finite element method. Basing on the asymptotic theory of vortex resistance a perturbation method applicable for determining the fluid oscillation damping in tanks of arbitrary shape with partitions of small relative width is developed.Oscillations of a cylinder beneath an ice cover in the neighborhood of a vertical wallhttps://www.zbmath.org/1475.760152022-01-14T13:23:02.489162Z"Tkacheva, L. A."https://www.zbmath.org/authors/?q=ai:tkacheva.l-aSummary: The solution to the problem of oscillations of a circular cylinder in fluid of finite depth beneath an ice cover in the neighborhood of a vertical wall is obtained. The ice cover is simulated by a thin elastic semi-infinite plate of constant thickness. Different boundary conditions at the plate edge are considered, namely, the free and clamped edges. The added mass and damping coefficients, the deflection and strain amplitudes of the ice cover, and the forces exerted on the wall are investigated depending on the oscillation frequency and input parameters of the problem.Resonant waves in the gap between two advancing bargeshttps://www.zbmath.org/1475.760162022-01-14T13:23:02.489162Z"Li, Liang"https://www.zbmath.org/authors/?q=ai:li.liang"Yuan, Zhiming"https://www.zbmath.org/authors/?q=ai:yuan.zhiming"Ji, Chunyan"https://www.zbmath.org/authors/?q=ai:ji.chunyan"Gao, Yan"https://www.zbmath.org/authors/?q=ai:gao.yanSummary: The gap resonance between two advancing rectangular barges in side-by-side arrangement is investigated using a 3-D Rankine source method. A modified Sommerfeld radiation condition accounting for Doppler shift is applied for the low forward speed problem when the scattered waves could propagate ahead of the barges. Numerical studies are conducted to investigate various factors which will influence the wave resonance in the narrow gap with particular attention paid on the forward speed effect and its coupling effects with gap width and draft. It is found that in the absence of forward speed, the trapped water surface oscillates like a flexible plate and the wave flow within the gap behaves like a standing wave. When the two barges are travelling ahead, the resonant wave patterns within the gap are reshaped. Additionally, the resonant frequencies shift to lower value and are compressed within a narrow range. Gap resonances are reduced by the augment of gap width. The effect of draft is shown to be associated with resonant modes. Draft effect becomes less pronounced at higher order resonant modes. Furthermore, both gap width and draft effects on gap resonance are found to be independent from forward speed.Multiscale rotating vortex patches for 2D Euler flows in a diskhttps://www.zbmath.org/1475.760172022-01-14T13:23:02.489162Z"Wan, Jie"https://www.zbmath.org/authors/?q=ai:wan.jieSummary: In this paper, we study the desingularization of multiscale rotating vortex patches with fixed angular velocity to the 2D Euler equations in a disk. We prove the existence of two-parameter multiscale V-states concentrating near two points. These two points are determined by the Robin function to the Green's function, the Green's function and angular velocity, and not symmetric about the origin, which is new to the former results. The existence of multiscale V-states with \(N\)-folds for \(N\ge 2\) is also proved.Harmonic internal waves in a semi-infinite stratified medium with shear flowshttps://www.zbmath.org/1475.760182022-01-14T13:23:02.489162Z"Bulatov, V. V."https://www.zbmath.org/authors/?q=ai:bulatov.vasily-v|bulatov.vitalii-vasilevich"Vladimirov, Yu. V."https://www.zbmath.org/authors/?q=ai:vladimirov.yu-v|vladimirov.yury-vSummary: The problem of constructing the solutions that describe harmonic internal gravity waves in a semi-infinite stratified medium with shear flow is considered. The model constant distribution of the Brunt-Väisälä frequency and the linear dependence of shear flow as functions of the depth are used and an analytical solution of the problem expressed in terms of the modified Bessel functions of the imaginary index is obtained. The analytical expressions for the dispersion relations are obtained using the Debye asymptotics of the modified Bessel function of the imaginary index and the phase characteristics of the wave fields are investigated. The wave characteristics of the excited fields are investigated as functions of the main parameters of the used stratification models, flows, and generation regimes.Anomalous dissipation, anomalous work, and energy balance for the Navier-Stokes equationshttps://www.zbmath.org/1475.760192022-01-14T13:23:02.489162Z"Cheskidov, Alexey"https://www.zbmath.org/authors/?q=ai:cheskidov.alexey"Luo, Xiaoyutao"https://www.zbmath.org/authors/?q=ai:luo.xiaoyutaoSolutions to the incompressible Navier-Stokes equations are considered on the \(d\)-dimensional torus, \(d\ge3\), which are regular on \((0,T)\) with possible violation of the energy balance in the limit \(t\to T\), \(t>T\). Notably, the external force is also present.
The authors investigate several scenarios in which the energy is lost either due to the convective nonlinearity (``anomalous dissipation''), or because of the (irregular) external force (the so-called ``anomalous work''). It turns out that these effects are independent: either of them can occur, and they can even cancel each other. The constructions are optimal in view of the Onsager regularity class.
Reviewer: Dalibor Prazak (Praha)On the large-time behavior of Euler-Poisson/Navier-Stokes equationshttps://www.zbmath.org/1475.760202022-01-14T13:23:02.489162Z"Choi, Young-Pil"https://www.zbmath.org/authors/?q=ai:choi.young-pil"Jung, Jinwook"https://www.zbmath.org/authors/?q=ai:jung.jinwookSummary: In this paper, we study the large-time behavior of charged particles interacting with the incompressible viscous flow. More precisely, we consider the isothermal/pressureless Euler-Poisson system coupled with the incompressible Navier-Stokes system through the drag force. Under suitable assumptions on the regularity of solutions, we show the fluid velocities are aligned with each other and the fluid density converges to the background state exponentially fast as time tends to infinity.Kinematics of viscous fluid flow during the filling of a pipe with a coaxial central bodyhttps://www.zbmath.org/1475.760212022-01-14T13:23:02.489162Z"Borzenko, E. I."https://www.zbmath.org/authors/?q=ai:borzenko.evgeny-i"Shrager, G. R."https://www.zbmath.org/authors/?q=ai:shrager.g-rSummary: The flow of a viscous fluid with a free surface realized during the filling of a vertical round pipe with a coaxial central body in the gravity field is numerically simulated. The mathematical formulation of the problem includes the Navier-Stokes and continuity equations discretized using the control volume method, together with the correcting SIMPLE procedure. The natural boundary conditions on the free surface are satisfied by means of the method of invariants. A parametric investigation of the filling process is carried out. The criterial dependences of the free surface shape parameters on the main dimensionless parameters of the problem are obtained. The mass distribution pattern is studied.On the description of some anisotropic viscous fluids by the methods of stochastic analysis on the groups of diffeomorphismshttps://www.zbmath.org/1475.760222022-01-14T13:23:02.489162Z"Gliklikh, Yuri E."https://www.zbmath.org/authors/?q=ai:gliklikh.yuri-e"Zalygaeva, Marina E."https://www.zbmath.org/authors/?q=ai:zalygaeva.marina-eSummary: In the framework of Lagrangian approach to hydrodynamics we suggest a special stochastic perturbation of the flow of perfect incompressible fluid on flat \(n\)-dimensional torus \(\mathcal{T}^n\) and obtain the description of viscous incompressible fluid with viscous term in the form of some second order differential operator more general than Laplacian. This model describes anisotropic fluids. We show that transition to Euler description of such a fluid yields the solution of an analogue of Navier-Stokes equation without external force.Axisymmetric Stokes flow around a sphere translating along the axis of a circular cylinderhttps://www.zbmath.org/1475.760232022-01-14T13:23:02.489162Z"Jeong, Jae-Tack"https://www.zbmath.org/authors/?q=ai:jeong.jae-tackSummary: We investigate the axisymmetric slow viscous flow around a sphere located on the axis of a long circular cylinder analytically based on the Stokes approximation. The sphere translates along the centerline of the cylinder with a constant velocity within Hagen-Poiseuille flow flowing far from the sphere. The translating velocity of the sphere and mean velocity of the Hagen-Poiseuille flow are arbitrary constant. To analyze Stokes equation, we use the method of complex eigenfunction expansions and the method of least squared error. As results, the streamline patterns and the pressure contour lines in the flow field are drawn for some radii of the sphere. The drag exerted on the sphere and the pressure change by the sphere are determined as the radius of the sphere. For a small sphere radius and for a sphere fitted closely in the cylinder, we compared results with previous asymptotic results and lubrication theory results, respectively. The velocity of the drifting sphere by the Hagen-Poiseuille flow in the circular cylinder is determined as the sphere radius. The pressure change induced by the drifting sphere in the Hagen-Poiseuille flow is also obtained. When the sphere translates along the plugged circular cylinder, a series of viscous toroidal eddies appears each side of the cylinder expectedly. Moreover, we discussed the pressure and shear stress on the sphere surface and showed some critical range of these stresses.Stokes flow around a hypersphere in \(n\)-dimensional space and its visualizationhttps://www.zbmath.org/1475.760242022-01-14T13:23:02.489162Z"Yoshino, Takashi"https://www.zbmath.org/authors/?q=ai:yoshino.takashiSummary: We derived the Stokes equations and velocity potential around a hyperspherical obstacle in \(n\)-dimensional space. The objectives of this study were to understand the hyperspace through the physics in the space and to bring the analytical solution of fluid flow in hyperspace for numerical simulation. The equations were obtained from the \(n\)-dimensional Navier-Stokes equation assuming the low Reynolds number flow. These were generalized formulae from a 3-dimensional system to an \(n\)-dimensional one. Our results show that the effect of the hyperspherical obstacle on the uniform flow is localized in higher dimensional spaces. We visualized the flow using the collections of hypersections.Axisymmetric creeping motion caused by a spherical particle in a micropolar fluid within a nonconcentric spherical cavityhttps://www.zbmath.org/1475.760252022-01-14T13:23:02.489162Z"Sherief, H. H."https://www.zbmath.org/authors/?q=ai:sherief.hany-h"Faltas, M. S."https://www.zbmath.org/authors/?q=ai:faltas.m-s"El-Sapa, Shreen"https://www.zbmath.org/authors/?q=ai:el-sapa.shreenSummary: The problems of the quasisteady translation and steady rotation of a solid spherical particle located at a non-concentric position of a spherical cavity filled with an incompressible micropolar fluid are investigated semi-analytically in the limit of low Reynolds numbers. General solutions are constructed from the superposition of the basic solutions in the two spherical coordinate systems based at the centers of the particle and cavity. The boundary conditions on the particle surface and cavity wall are satisfied by a collocation numerical method. The hydrodynamic drag force and torque exerted by the fluid on the particle which are proportional to the translational and angular velocities respectively are obtained numerically with good convergence for a range of values of the ratio of particle-to-cavity radii, the relative distance between the centers of the particle and cavity and micropolarity parameter. In the limit of the motion of a spherical particle in a concentric position in the cavity and in the lubrication limit, the hydrodynamic drag force and torque are in good agreement with the available results in the literature. As expected, the boundary-corrected drag force and torque exerted on the particle is a monotonic increasing function of the micropolarity parameter.Suction controlled topological transition in laminar juncture flowshttps://www.zbmath.org/1475.760262022-01-14T13:23:02.489162Z"Hu, B."https://www.zbmath.org/authors/?q=ai:hu.baoan|hu.bambi|hu.bingzhong|hu.bijin|hu.bei|hu.baiqing|hu.biaobiao|hu.beibei|hu.bowen|hu.baosheng|hu.biao|hu.bang|hu.busong|hu.biyu|hu.baocun|hu.binbin|hu.bixin|hu.binglu|hu.bingsong|hu.bing|hu.bizhong|hu.baozhu|hu.bitao|hu.baiding|hu.brian|hu.bingyang|hu.benqiong|hu.baolin|hu.boxing|hu.binxin|hu.botao|hu.bangyou|hu.bingmin|hu.bingjie|hu.bingquan|hu.boxia|hu.baoqing|hu.baomin|hu.baoli|hu.baogang|hu.benyong|hu.beihua|hu.benmu|hu.beilai|hu.baokun|hu.binjie|hu.bo|hu.bin|hu.baihui|hu.bingran|hu.baohua|hu.baowen"Zhang, H."https://www.zbmath.org/authors/?q=ai:zhang.haowei|zhang.hongkui|zhang.huanan|zhang.huqin|zhang.hongqiu|zhang.huaxiao|zhang.haiqun|zhang.hongwang|zhang.huiqun|zhang.hongching|zhang.haijiang|zhang.honglu|zhang.huiting|zhang.huapeng.1|zhang.huachun|zhang.huabo|zhang.heping|zhang.hengjie|zhang.hongli|zhang.hongtn|zhang.hongda|zhang.huanping|zhang.huixing|zhang.hongxiang|zhang.hongqian|zhang.hantao|zhang.haijian|zhang.haimiao|zhang.huang|zhang.haiyan|zhang.hongyu|zhang.haoyong|zhang.hanguo|zhang.honglue|zhang.hongpeng|zhang.hexin|zhang.huishi|zhang.huanchun|zhang.haiyong|zhang.hongjie|zhang.handong|zhang.haie|zhang.haofeng|zhang.huayan|zhang.huali|zhang.hongke|zhang.hanze|zhang.hao.2|zhang.hanqian|zhang.huarong|zhang.hua|zhang.hejin|zhang.heyi|zhang.huakai|zhang.hongchen|zhang.haili|zhang.haohui|zhang.haisu|zhang.haiying|zhang.hai.4|zhang.honghao|zhang.huapeng|zhang.haltau|zhang.houchao|zhang.hanhua|zhang.hui.4|zhang.huijun|zhang.hanjiang|zhang.hongmin|zhang.huixian|zhang.hongxu|zhang.heying|zhang.haoyan|zhang.hongsheng|zhang.huaizhou|zhang.huanying|zhang.huan|zhang.huashuo|zhang.haisen|zhang.huilin|zhang.hongce|zhang.huongwei|zhang.huidi|zhang.han|zhang.hongsong|zhang.huiping|zhang.huichun|zhang.haoyu|zhang.haiqiang|zhang.hui.11|zhang.hailun|zhang.heyu|zhang.hanwang|zhang.haolong|zhang.heng|zhang.hongqi|zhang.huigang|zhang.huazhu|zhang.huixi|zhang.haikuan|zhang.hongyan|zhang.huachen|zhang.huifu|zhang.hong-jiang|zhang.haifang|zhang.huanqiang|zhang.hongning|zhang.haihui|zhang.huimei|zhang.hangke|zhang.hailing|zhang.hongyou|zhang.hairong|zhang.huaqiao|zhang.hongbin|zhang.hanghui|zhang.haixia|zhang.huilong|zhang.haiping|zhang.hui.6|zhang.hao|zhang.huaqing|zhang.huadong|zhang.huipeng|zhang.hui.1|zhang.haoran|zhang.hebiao|zhang.hongqing.1|zhang.huai|zhang.hanzhuang|zhang.houlei|zhang.huilan|zhang.honglai|zhang.huaxi|zhang.haiyang|zhang.huabiao|zhang.hao.4|zhang.hehong|zhang.haiou|zhang.hongshen|zhang.haochuan|zhang.huaizhong|zhang.hongrui|zhang.hanshuo|zhang.huazong|zhang.huaiyu|zhang.hongying|zhang.huming|zhang.hangguo|zhang.haonan|zhang.haibiao|zhang.hongduan|zhang.huijuan|zhang.hai.2|zhang.hanmou|zhang.huaixiang|zhang.huayue|zhang.huafeng|zhang.huiqiao|zhang.hongtu|zhang.huxing|zhang.hanyuan|zhang.hongfen|zhang.hongmei|zhang.hou|zhang.hanbin|zhang.huichai|zhang.hongying.1|zhang.hainan|zhang.hongming|zhang.honglian|zhang.haixiang|zhang.hangwei|zhang.huilai|zhang.huiyu|zhang.hongtao|zhang.huiju|zhang.huiwen|zhang.huainian|zhang.hui.3|zhang.hai|zhang.haiqiao|zhang.huaixin|zhang.haibin|zhang.huiqiu|zhang.huaguang.1|zhang.huwei|zhang.haini|zhang.huaxiong|zhang.hongguang|zhang.hongbiao|zhang.haipeng|zhang.hongqin|zhang.hai.3|zhang.hezi|zhang.haiwei|zhang.hanqing|zhang.hehua|zhang.haozhong|zhang.hanqin|zhang.hanzhou|zhang.hedan|zhang.huiran|zhang.haiwen|zhang.haiyuan|zhang.hui.9|zhang.hongwe|zhang.hongqiang|zhang.houxian|zhang.haoyuan|zhang.hangfu|zhang.haolan|zhang.hengjun|zhang.huiyan|zhang.huimin|zhang.hanwei|zhang.huanren|zhang.hongchao|zhang.hanzhe|zhang.hao.3|zhang.hongling|zhang.haizhang|zhang.hujun|zhang.huanyu|zhang.haiyin|zhang.hongwu|zhang.huaao|zhang.huanjun|zhang.huaqiang|zhang.huoming|zhang.huajia|zhang.huayang|zhang.hongjian|zhang.hiaying|zhang.hongyuan|zhang.huizhen|zhang.hanwen|zhang.harry|zhang.haijuan|zhang.haiquan|zhang.heting|zhang.huancheng|zhang.huawei|zhang.hanling|zhang.haitao|zhang.hongjuan|zhang.hanpeng|zhang.haimo|zhang.huirong|zhang.hongna|zhang.haoqiang|zhang.hongkai|zhang.hu|zhang.hualei|zhang.huiliang|zhang.huajie|zhang.haiqing|zhang.huining|zhang.hefa|zhang.hongchuan|zhang.hongbuo|zhang.hanzhi|zhang.haochen|zhang.hongran|zhang.huishuai|zhang.honghong|zhang.haihong|zhang.huiquan|zhang.houle|zhang.huile|zhang.hongxun|zhang.huiguo|zhang.honghua|zhang.haifeng|zhang.huaifeng|zhang.huanli|zhang.haichao|zhang.huizhan|zhang.haibing|zhang.honglin|zhang.haobo|zhang.haimeng|zhang.huili|zhang.huiru|zhang.huizeng|zhang.hongshui|zhang.haozhe|zhang.hang|zhang.hongbing|zhang.haibo|zhang.hanfang|zhang.huamin|zhang.hongfei|zhang.huisheng|zhang.huiying|zhang.honggang|zhang.henghai|zhang.honghai|zhang.hongliang|zhang.he|zhang.hanbin.1|zhang.huixia|zhang.haiming|zhang.huibing|zhang.huifang|zhang.hongyun|zhang.haoqi|zhang.huasheng|zhang.huanlong|zhang.haiyi|zhang.huaping|zhang.hongyang|zhang.haolu|zhang.huanhao|zhang.huaxin|zhang.hengdi|zhang.haomin|zhang.hanquan|zhang.huangwei|zhang.hongzhen|zhang.hanjie|zhang.haotian|zhang.haochun|zhang.hongjun|zhang.haidi|zhang.hui.10|zhang.hongbo|zhang.haijun|zhang.henggui|zhang.haijin|zhang.hongfan|zhang.honghan|zhang.housheng|zhang.huizhi|zhang.haoyue|zhang.huiqiang|zhang.heping.2|zhang.hui|zhang.hengbin|zhang.haidong|zhang.haowen|zhang.huina|zhang.hanlin|zhang.hongping|zhang.houzhong|zhang.hongxin|zhang.hanming|zhang.huixiang|zhang.hongyue|zhang.huanguo|zhang.huiqin|zhang.huayong|zhang.haiqi|zhang.huaiqing|zhang.huanshui|zhang.heni|zhang.huitao|zhang.hairui|zhang.hongde|zhang.haopeng|zhang.haicang|zhang.haodong|zhang.haiyun|zhang.huajun|zhang.haoyun|zhang.hongqing|zhang.hongye|zhang.huayun|zhang.hailiang|zhang.haojie|zhang.huaguang|zhang.haiting|zhang.hechun|zhang.hanjun|zhang.houjun|zhang.hongquan|zhang.huiyuan|zhang.hongyi|zhang.hanxin|zhang.huanling|zhang.hui.7|zhang.huaihong|zhang.haina|zhang.haideng|zhang.haicheng|zhang.hesheng|zhang.hengyan|zhang.hailan|zhang.hengmin|zhang.huanhuan|zhang.haizheng|zhang.huajuan|zhang.haozhi|zhang.huaide|zhang.haishan|zhang.henglong|zhang.haoqian|zhang.hengtao|zhang.hejia|zhang.huifeng|zhang.hualian|zhang.huiyang|zhang.hudong|zhang.huaijian|zhang.huaxiang|zhang.huiming|zhang.hailin|zhang.hongcai|zhang.hanqiu|zhang.huaren|zhang.heping.1|zhang.huaige|zhang.huiling|zhang.huijie|zhang.hongzhong|zhang.hui.2|zhang.hao.1|zhang.hanxiao|zhang.hongbao|zhang.huaipin|zhang.haixu|zhang.hongzhi|zhang.hewei|zhang.huiliu|zhang.haixian|zhang.huipin|zhang.hui.5|zhang.haigang|zhang.hongkun|zhang.huizhong|zhang.huantao|zhang.hongwei.1|zhang.hongwei.2|zhang.haoliang|zhang.hong.6|zhang.hongjing|zhang.haijie|zhang.hongbo.1|zhang.heming|zhang.huidong|zhang.hengxu|zhang.hongfu|zhang.hanxiong|zhang.huihua|zhang.huaiqiang|zhang.huaiwu|zhang.honggao|zhang.honghui|zhang.hanbing|zhang.huiqing|zhang.hengyun|zhang.huazhong|zhang.hui.8|zhang.hemiao|zhang.huike|zhang.haodi|zhang.hongxia|zhang.huaiye|zhang.huaixiong|zhang.hualong|zhang.hailong|zhang.huaming|zhang.hanrui|zhang.huisen|zhang.huaan|zhang.huihui|zhang.huiyun|zhang.huikai|zhang.hai.1|zhang.haixing|zhang.honglei|zhang.hongwen|zhang.haixin|zhang.hoingqian|zhang.heye|zhang.hanyu|zhang.huanwei|zhang.huaibao|zhang.huizhu|zhang.huaiyue"Younis, M. Y."https://www.zbmath.org/authors/?q=ai:younis.m-ySummary: The effect of suction on the topological transition in juncture flow is studied experimentally and numerically. A number of combinations of the positions, where suction is applied, and the flow rates are investigated and their effect on the topological transition of laminar juncture flow is assessed. It is observed that for any particular case, a combination of suction hole positions and volume flow rates can transform the most upstream surface singular point of the horseshoe vortex (HSV) system from a saddle of separation to a saddle of attachment. The topological transition at low suction rates is achieved, when the suction holes are placed close to the separation region. A better HSV control is achieved, when suction is applied close to the juncture at high suction rates. A previously proposed separation/attachment prediction method based on the mass conservation is also confirmed by analyzing the simulated results of suction-controlled and originally-generated wall saddles. The results suggest that the topological transition (separation/attachment) at each wall saddle can be accurately estimated according to the sign of a discriminant coefficient \(C_{S/A}\) comprised of the local shear stress \(\tau_w\) on the wall and stream-tube width \(n\) near the saddle.An experimental investigation of vortex-induced vibration of a curved flexible cylinderhttps://www.zbmath.org/1475.760272022-01-14T13:23:02.489162Z"Seyed-Aghazadeh, Banafsheh"https://www.zbmath.org/authors/?q=ai:seyed-aghazadeh.banafsheh"Benner, Bridget"https://www.zbmath.org/authors/?q=ai:benner.bridget"Gjokollari, Xhino"https://www.zbmath.org/authors/?q=ai:gjokollari.xhino"Modarres-Sadeghi, Yahya"https://www.zbmath.org/authors/?q=ai:modarres-sadeghi.yahyaSummary: Vortex-induced vibration of a curved flexible cylinder placed in the test section of a recirculating water tunnel and fixed at both ends is studied experimentally. Both the concave and the convex orientations (with respect to the incoming flow direction) are considered. The cylinder was hung by its own weight with a dimensionless radius of curvature of \(R/D=66\), and a low mass ratio of \(m^* = 3.6\). A high-speed imaging technique was employed to record the oscillations of the cylinder in the cross-flow direction for a reduced velocity range of \(U^* = 3.7\)--48.4, corresponding to a Reynolds number range of \(Re= 165\)--2146. Mono- and multi-frequency responses as well as transition from low-mode-number to high-mode-number oscillations were observed. Regardless of the type of curvature, both odd and even mode shapes were excited in the cross-flow directions. However, the response of the system, in terms of the excited modes, amplitudes and frequencies of the oscillations, was observed to be sensitive to the direction of the curvature (i.e. concave vs convex), in particular at higher reduced velocities, where mode transition occurred. Hydrogen bubble flow visualization exhibited highly three-dimensional vortex shedding patterns in the wake of the cylinder, where there existed spatial and temporal evolution of the vortex shedding modes along the length of the cylinder. The time-varying intermittent vortex shedding in the wake of the cylinder was linked to the spanwise travelling wave behaviour of the vortex-induced vibration response. The observed spatially altering wake corresponded to the multi-modal excitation and mode transition along the length of the cylinder.A structural bifurcation analysis of flow phenomenon for shear flow past an inclined square cylinder: application to 2D unsteady separationhttps://www.zbmath.org/1475.760282022-01-14T13:23:02.489162Z"Kumar, Atendra"https://www.zbmath.org/authors/?q=ai:kumar.atendra"Ray, Rajendra K."https://www.zbmath.org/authors/?q=ai:ray.rajendra-kSummary: A structural bifurcation analysis of an incompressible two-dimensional (2D) shear flow past an inclined square cylinder by considering topological properties of flow is done in this paper. We have shown how the flow separation leads to complex structure at a time from a point by using this analysis. The streamfunction-vorticity \((\Psi - \zeta)\) formulation of Navier-Stokes (N-S) equations in Cartesian coordinates is solved using a higher order compact (HOC) finite difference scheme. Through this analysis, we capture the exact locations of first and second bifurcation points with appropriate non-dimensional time of their occurrences for initial stages as well as fully developed flow. The flow field is mainly influenced by Reynolds number, Re, and shear rate, \(\kappa\). It is shown that the first and second bifurcations developed within a very small time difference from the upper and lower downstream edges of the cylinder up to \(\kappa = 0.1\). Numerical simulations are carried out for Re = 100, 185 with \(\kappa\) values range from 0 to 0.4. The purpose of the present study is to elaborate on the influence of shear parameter on flow properties. The temporal behavior of vortex formation and relevant streakline patterns are scrutinized for all parameter values. Occurrence of multiple separations is demonstrated in detail by varying \(\kappa\) for both initial and fully developed flows. Comparisons with previous results in the literature clearly verify the accuracy and validity of the present work.Wake characteristics of a sphere performing transverse rotary oscillationshttps://www.zbmath.org/1475.760292022-01-14T13:23:02.489162Z"Manelil, Neeraj P."https://www.zbmath.org/authors/?q=ai:manelil.neeraj-p"Tiwari, Shaligram"https://www.zbmath.org/authors/?q=ai:tiwari.shaligramSummary: Three-dimensional numerical investigations have been carried out to study the unsteady wake behind a sphere performing transverse rotational oscillations. Frequency and amplitude of forced oscillation have been varied and their influence on coherent wake structures and transitions have been presented. These structures have been identified with the help of instantaneous iso-\(\lambda_2\) surfaces and streamline plots. The results reveal presence of different vortex shedding modes that appear over the parametric range. Variations in mean and instantaneous values of hydrodynamic coefficients with amplitude and frequency of forced oscillations have also been reported in this work. Time series signals of these force coefficients have been analysed using Hilbert Huang transformation and recurrence relations. These techniques shed light on the time dependent behaviour of the wake by providing insights on frequency-time-amplitude distributions of the wake oscillations. Nonlinearities in wake interactions have also been quantified in terms of degree of stationarity. Variation of recurrence quantification parameters with change in forcing frequency has also been presented.Evolution of wake structures behind oscillating hydrofoils with combined heaving and pitching motionhttps://www.zbmath.org/1475.760302022-01-14T13:23:02.489162Z"Verma, Suyash"https://www.zbmath.org/authors/?q=ai:verma.suyash"Hemmati, Arman"https://www.zbmath.org/authors/?q=ai:hemmati.armanSummary: The wake of an oscillating teardrop hydrofoil with combined heaving and pitching motion was studied numerically at Reynolds number of 8000 and Strouhal numbers of \(St=0.21\)--0.94. The lower Strouhal number exhibited high efficiency propulsion with small thrust generation. However, larger thrust generation at high \(St\) required more power, which lowered the propulsive efficiency. Quantitative assessment of vortex evolution, along with qualitative investigation of the formation and interaction of primary structures, revealed the association with elliptic instability characteristics for both co-rotating and counter-rotating vortex structures in both wakes. With respect to advection of the leading-edge vortex, the pressure distribution further depicted evidence of spanwise instability with distinct temporal evolution along the suction and pressure surfaces of the oscillating foil. Three-dimensional assessment of wake structures located downstream of the trailing edge depicted the existence of dislocations associated with primary vortex `rollers'. At low \(St\), these were limited to fine spanwise corrugations (valleys and bulges) on weaker leading edge rollers, which enlarged as the rollers advected downstream. In contrast, at high \(St\), the wake exhibited conjoint hairpin-horseshoe vortex structures that led to stronger deformations on the coupled vortex rollers. The statistical characteristics of secondary structures resembled the long wavelength mode and mode A identified previously for purely pitching and heaving foils, respectively. They also mimicked mode B for stationary cylinders. Novel wake models are introduced based on a complete vivid three-dimensional depiction of coherent wake structures.Virtual wave stress and transient mean drift in spatially damped long interfacial waveshttps://www.zbmath.org/1475.760312022-01-14T13:23:02.489162Z"Weber, Jan Erik H."https://www.zbmath.org/authors/?q=ai:weber.jan-erik-h"Christensen, Kai H."https://www.zbmath.org/authors/?q=ai:christensen.kai-haakonSummary: The mean drift in spatially damped long gravity waves at the boundary between two layers of immiscible viscous fluids is investigated theoretically by applying a Lagrangian description of motion. The focus of the paper is on the development of the drift near the interface. The initial drift (inviscid Stokes drift + viscous boundary-layer terms) associated with the instantaneously imposed wave field does not generally fulfill the conditions at the common boundary between the layers. Hence, transient Eulerian mean currents develop on both sides of the interface to ensure continuity of velocities and viscous stresses. The development of strong jet-like Eulerian currents increasing with time in this problem is related to the action of the virtual wave stress (VWS). Very soon (after a few wave periods) the transient Eulerian part dominates in the Lagrangian mean current. This effect is similar to that found for the drift in short gravity waves with a film-covered surface. A new relation is derived showing that the difference between the VWS's at the interface is given by the divergence of the total horizontal wave momentum flux in a two-layer system. Our analysis with spatially damped waves also yields the Lagrangian change of the mean surface level and mean interfacial level (the divergence effect) due to periodic baroclinic wave motion.Density distribution in the flow past a sphere descending in a salt-stratified fluidhttps://www.zbmath.org/1475.760322022-01-14T13:23:02.489162Z"Okino, Shinya"https://www.zbmath.org/authors/?q=ai:okino.shinya"Akiyama, Shinsaku"https://www.zbmath.org/authors/?q=ai:akiyama.shinsaku"Takagi, Koki"https://www.zbmath.org/authors/?q=ai:takagi.koki"Hanazaki, Hideshi"https://www.zbmath.org/authors/?q=ai:hanazaki.hideshiSummary: The density distribution around a sphere descending in a salt-stratified fluid is measured by the laser-induced fluorescence (LIF) method. The corresponding velocity distribution is measured by particle image velocimetry (PIV), and numerical simulation is also performed to supplement the observations by LIF and PIV. In steady flow, LIF observes a thin and vertically long structure which corresponds to a buoyant jet. The bell-shaped structure, which appears under strong stratification and moderate Reynolds number (Froude number \(Fr \lesssim 3\), Reynolds number \(50 \lesssim Re \lesssim 500\)), is also identified. The measured density distributions in the salinity boundary layer and in the jet agree with the numerical simulations which use the Schmidt number of the fluorescent dye (\(Sc \sim 2000\)). The initially unsteady process of the jet formation is also investigated. Under weak stratification, the LIF shows an initial development of an axisymmetric rear vortex as observed in homogeneous fluids. However, as time proceeds and the effect of stratification becomes significant, the vortex shrinks and disappears, while the jet extends vertically upward. Under strong stratification, a thin jet develops without generating a rear vortex, since the effect of stratification becomes significant in a short time before the vortex is generated.Autooscillations branched off from the neutral curve in the supersonic boundary layerhttps://www.zbmath.org/1475.760332022-01-14T13:23:02.489162Z"Gaponov, S. A."https://www.zbmath.org/authors/?q=ai:gaponov.s-a"Terekhova, N. M."https://www.zbmath.org/authors/?q=ai:terekhova.n-mSummary: The soft and hard regimes of generation of periodic fluctuations in the supersonic boundary layer at moderate (M = 2) and high (M = 5.35) Mach numbers are investigated within the framework of weakly nonlinear theory. The model includes both the effects of self-action which are inherent in incompressible fluid flows (generation of secondary steady-state harmonics and generation of double-frequency perturbations) and the cubic terms of original fluctuations appearing only for compressible gas. The study of the nature of generation of periodic regimes in the neighborhood of the neutral curve in compressible flows is useful since it can lead to new results that are necessary for understanding the laminar-turbulent transition laws.Optimal disturbances in the development of the instability of a free shear layer and a system of two counter-streaming jet flowshttps://www.zbmath.org/1475.760342022-01-14T13:23:02.489162Z"Kalashnik, M. V."https://www.zbmath.org/authors/?q=ai:kalashnik.m-v"Chkhetiani, O. G."https://www.zbmath.org/authors/?q=ai:chkhetiani.o-gSummary: An analytical approach to the determination of optimal disturbances is developed. The approach, suitable for flows with piecewise-constant vorticity distributions, is based on the equation of disturbance energy balance and explicit expressions for the growth rate of the energy or the final-to-initial energy ratio. The corresponding expressions are functions of the initial parameters and the optimal disturbance parameters are determined from an extremization of these functions. Within the framework of the approach the classical Rayleigh problem of the free shear layer instability and the problem of the instability of a system consisting of two counter-streaming jet flows in a rotating shallow water layer are considered. The parameters of the optimal disturbances are compared with those of growing normal modes.Effects of phase difference between instability modes on boundary-layer transitionhttps://www.zbmath.org/1475.760352022-01-14T13:23:02.489162Z"Kim, Minwoo"https://www.zbmath.org/authors/?q=ai:kim.minwoo"Kim, Seungtae"https://www.zbmath.org/authors/?q=ai:kim.seungtae"Lim, Jiseop"https://www.zbmath.org/authors/?q=ai:lim.jiseop"Lin, Ray-Sing"https://www.zbmath.org/authors/?q=ai:lin.ray-sing"Jee, Solkeun"https://www.zbmath.org/authors/?q=ai:jee.solkeun"Park, Donghun"https://www.zbmath.org/authors/?q=ai:park.donghunSummary: Phase effect on the modal interaction of flow instabilities is investigated for laminar-to-turbulent transition in a flat-plate boundary-layer flow. Primary and secondary three-dimensional (3-D) oblique waves at various initial phase differences between these two instability modes. Three numerical methods are used for a systematic approach for the entire transition process, i.e. before the onset of transition well into fully turbulent flow. Floquet analysis predicts the subharmonic resonance where a subharmonic mode locally resonates for a given basic flow composed of the steady laminar flow and the fundamental mode. Because Floquet analysis is limited to the resonating subharmonic mode, nonlinear parabolised stability equation analysis (PSE) is conducted with various phase shifts of the subharmonic mode with respect to the given fundamental mode. The application of PSE offers insights on the modal interaction affected by the phase difference up to the weakly nonlinear stage of transition. Large-eddy simulation (LES) is conducted for a complete transition to turbulent boundary layer because PSE becomes prohibitively expensive in the late nonlinear stage of transition. The modulation of the subharmonic resonance with the initial phase difference leads to a significant delay in the transition location up to \(\Delta Re_{x, tr} \simeq 4\times 10^5\) as predicted by the current LES. Effects of the initial phase difference on the spatial evolution of the modal shape of the subharmonic mode are further investigated. The mechanism of the phase evolution is discussed, based on current numerical results and relevant literature data.Entrainment and growth of vortical disturbances in the channel-entrance regionhttps://www.zbmath.org/1475.760362022-01-14T13:23:02.489162Z"Ricco, Pierre"https://www.zbmath.org/authors/?q=ai:ricco.pierre"Alvarenga, Claudia"https://www.zbmath.org/authors/?q=ai:alvarenga.claudiaSummary: The entrainment of free-stream unsteady three-dimensional vortical disturbances in the entry region of a channel is studied via matched asymptotic expansions and by numerical means. The interest is in flows at Reynolds numbers where experimental studies have documented the occurrence of intense transient growth, despite the flow being stable according to classical stability analysis. The analytical description of the vortical perturbations at the channel mouth reveals how the oncoming disturbances penetrate into the wall-attached shear layers and amplify downstream. The effects of the channel confinement, the streamwise pressure gradient and the viscous/inviscid interplay between the oncoming disturbances and the boundary-layer perturbations are discussed. The composite perturbation velocity profiles are employed as initial conditions for the unsteady boundary-region perturbation equations. At a short distance from the channel mouth, the disturbance flow is mostly confined within the shear layers and assumes the form of streamwise-elongated streaks, while farther downstream the viscous disturbances permeate the whole channel although the base flow is still mostly inviscid in the core. Symmetrical disturbances exhibit a more significant growth than anti-symmetrical disturbances, the latter maintaining a nearly constant amplitude for several channel heights downstream before growing transiently, a unique feature not reported in open boundary layers. The disturbances are more intense as the frequency decreases or the bulk Reynolds number increases. We compute the spanwise wavelengths that cause the most intense downstream growth and the threshold wall-normal wavelengths below which the perturbations are damped through viscous dissipation.Linear temporal instability analysis of a non-Newtonian liquid jet containing cavitation bubbleshttps://www.zbmath.org/1475.760372022-01-14T13:23:02.489162Z"Wang, Xin-Tao"https://www.zbmath.org/authors/?q=ai:wang.xin-tao"Ning, Zhi"https://www.zbmath.org/authors/?q=ai:ning.zhi"Lü, Ming"https://www.zbmath.org/authors/?q=ai:lu.mingSummary: The temporal instability behavior of a non-Newtonian liquid jet in the presence of cavitation bubbles is investigated theoretically. The power law model is selected to describe the viscosity of the non-Newtonian jet. The unstable growth rate is obtained by Chebyshev collocation method. Besides, the effects of the compressibility of liquid, the compressibility of gas, the incorporating compressibility of both liquid and gas on the instability of the power law liquid jet are studied in this case. Especially, energy analysis is performed to study the breakup mechanism of the jet. The results show that the liquid compressibility is a unstable factor on the jet instability. However, the gas compressibility is the factor to prevent the jet from breaking. For the axisymmetric disturbance, it is noted that the viscous force always makes the jet being stable by energy analysis. But for the first asymmetric disturbance, there exists a turning point for the effect of viscosity of the liquid on the jet instability at a large wave number.Effect of anisotropy on the onset of convection in rotating bi-disperse Brinkman porous mediahttps://www.zbmath.org/1475.760382022-01-14T13:23:02.489162Z"Capone, Florinda"https://www.zbmath.org/authors/?q=ai:capone.florinda"De Luca, Roberta"https://www.zbmath.org/authors/?q=ai:de-luca.roberta"Massa, Giuliana"https://www.zbmath.org/authors/?q=ai:massa.giulianaSummary: Thermal convection in a horizontally isotropic bi-disperse porous medium (BDPM) uniformly heated from below is analysed. The combined effects of uniform vertical rotation and Brinkman law on the stability of the steady state of the momentum equations in a BDPM are investigated. Linear and nonlinear stability analysis of the conduction solution is performed, and the coincidence between linear instability and nonlinear stability thresholds in the \(L^2\)-norm is obtained.Maxwell-Cattaneo double-diffusive convection: limiting caseshttps://www.zbmath.org/1475.760392022-01-14T13:23:02.489162Z"Hughes, D. W."https://www.zbmath.org/authors/?q=ai:hughes.david-wynne"Proctor, M. R. E."https://www.zbmath.org/authors/?q=ai:proctor.michael-r-e"Eltayeb, I. A."https://www.zbmath.org/authors/?q=ai:eltayeb.ibrahim-aSummary: Double-diffusive convection, in which a fluid is acted upon by two fields (such as temperature and salinity) that affect the density, has been widely studied in areas as diverse as the oceans and stellar atmospheres. Assuming classical Fickian diffusion for both heat and salt, the evolution of temperature and salinity are governed by parabolic advection-diffusion equations. In reality, there are small extra terms in these equations that render the equations hyperbolic (the Maxwell-Cattaneo effect). Although these corrections are nominally small, they represent a singular perturbation and hence can lead to significant effects when the underlying differences of salinity and temperature are large. In this paper, we investigate the linear stability of a double-diffusive fluid layer and show that amending Fick's law for the temperature, or the salinity, alone can lead to new modes of oscillation and to very large changes in the preferred wavelength of oscillatory convection at onset. In particular, the salt finger regime of classical double diffusion is here replaced by Maxwell-Cattaneo oscillations when the salt concentration is very high. The more complicated case when both laws are amended is left to a future paper, now in preparation.Stability of advective flow in a horizontal incompressible fluid layer in the presence of the Navier slip conditionhttps://www.zbmath.org/1475.760402022-01-14T13:23:02.489162Z"Schwarz, K. G."https://www.zbmath.org/authors/?q=ai:schwarz.k-g"Schwarz, Yu. A."https://www.zbmath.org/authors/?q=ai:schwarz.yu-aSummary: The exact solution of the Navier-Stokes equations in the Boussinesq approximation that describes plane-parallel advective flow in the plane incompressible fluid layer with horizontal boundaries on which the Navier slip condition and the linear temperature distribution are specified is given. The behavior of the velocity and temperature with increase in the slip parameter is considered. The stability of advective flow with respect to plane and spiral perturbations is investigated within the framework of the linear theory. Finite-amplitude perturbations in the supercritical domain in the neighborhood of minima of neutral curves are studied within the framework of the nonlinear formulation of the problem.Comparison of the effects of three types of time-periodic body force on linear and non-linear stability of convection in nanoliquidshttps://www.zbmath.org/1475.760412022-01-14T13:23:02.489162Z"Siddheshwar, P. G."https://www.zbmath.org/authors/?q=ai:siddheshwar.pradeep-g"Meenakshi, N."https://www.zbmath.org/authors/?q=ai:meenakshi.nSummary: The effect of three different types of time-periodic vertical oscillations of the Rayleigh-Bénard system involving Newtonian nanoliquids is studied in the paper. Twenty nanoliquids are considered for investigation and it is found that enhanced heat transport is seen in all of them compared to what is observed in the corresponding carrier liquids without the nanoparticles. The increase in the amplitude of the vertical vibration is shown to augment convection in the nanoliquids whereas increase in frequency is to inhibit convection. On comparing the extent of heat transport in the presence of modulation with that in its absence, it was found that heat transport diminished in the former case. It was also found that the trigonometric sine type of gravity modulation transports heat intermediate to that of triangular and square types. The triangular type inhibits heat transport while square type enhances heat transport leading one to conclude that heat transport in a Rayleigh-Bénard system can be enhanced by using a combination of dilute concentration of nanoparticles and gravity modulation using a square wave.Thermosolutal convection with a Navier-Stokes-Voigt fluidhttps://www.zbmath.org/1475.760422022-01-14T13:23:02.489162Z"Straughan, Brian"https://www.zbmath.org/authors/?q=ai:straughan.brianSummary: We present a model for convection in a Navier-Stokes-Voigt fluid when the layer is heated from below and simultaneously salted from below, the thermosolutal convection problem. Instability thresholds are calculated for thermal convection with a dissolved salt field in a complex viscoelastic fluid of Navier-Stokes-Voigt type. The Kelvin-Voigt parameter is seen to play a very important role in acting as a stabilizing agent when the convection is of oscillatory type. The quantitative size of this effect is displayed. Nonlinear stability is also discussed, and it is briefly indicated how the global nonlinear stability limit may be increased, although there still remains a region of potential sub-critical instability, especially when the Kelvin-Voigt parameter increases.Instabilities and sensitivities in a flow over a rotationally flexible cylinder with a rigid splitter platehttps://www.zbmath.org/1475.760432022-01-14T13:23:02.489162Z"Basso, R. L. G."https://www.zbmath.org/authors/?q=ai:basso.r-l-g"Hwang, Y."https://www.zbmath.org/authors/?q=ai:hwang.youngdeok|hwang.yongho|hwang.yongwoo|hwang.youngkyu|hwang.yoongu|hwang.yau|hwang.yonghun|hwang.yousub|hwang.yoonseok|hwang.youngjin|hwang.yongsoo|hwang.yongyun|hwang.youngho|hwang.yuhchang"Assi, G. R. S."https://www.zbmath.org/authors/?q=ai:assi.gustavo-r-s"Sherwin, S. J."https://www.zbmath.org/authors/?q=ai:sherwin.spencer-jSummary: This paper investigates the origin of flow-induced instabilities and their sensitivities in a flow over a rotationally flexible circular cylinder with a rigid splitter plate. A linear stability and sensitivity problem is formulated in the Eulerian frame by considering the geometric nonlinearity arising from the rotational motion of the cylinder which is not present in the stationary or purely translating stability methodology. This nonlinearity needs careful and consistent treatment in the linearised problem particularly when considering the Eulerian frame or reference adopted in this study that is not so widely considered. Two types of instabilities arising from the fluid-structure interaction are found. The first type of instabilities is the stationary symmetry breaking mode, which was well reported in previous studies. This instability exhibits a strong correlation with the length of the recirculation zone. A detailed analysis of the instability mode and its sensitivity reveals the importance of the flow near the tip region of the plate for the generation and control of this instability mode. The second type is an oscillatory torsional flapping mode, which has not been well reported. This instability typically emerges when the length of the splitter plate is sufficiently long. Unlike the symmetry breaking mode, it is not so closely correlated with the length of the recirculation zone. The sensitivity analysis however also reveals the crucial role played by the flow near the tip region in this instability. Finally, it is found that many physical features of this instability are reminiscent of those of the flapping (or flutter instability) observed in a flow over a flexible plate or a flag, suggesting that these instabilities share the same physical origin.Non-modal Floquet stability of capsules in large-amplitude oscillatory extensional flowhttps://www.zbmath.org/1475.760442022-01-14T13:23:02.489162Z"Bryngelson, Spencer H."https://www.zbmath.org/authors/?q=ai:bryngelson.spencer-h"Freund, Jonathan B."https://www.zbmath.org/authors/?q=ai:freund.jonathan-bSummary: We analyze the stability of a capsule in large-amplitude oscillatory extensional (LAOE) flow, as often used to study the rheology and dynamics of suspensions. Such a flow is typically established in a cross-slot configuration, with the particle (or particles) of interest observed in the stagnation region. However, controlling this configuration is challenging because the flow is unstable. We quantify such an instability for spherical elastic capsules suspended near the stagnation point using a non-modal global Floquet analysis, which is formulated to include full coupling of the capsule-viscous-flow dynamics. The flow is shown to be transiently, though not asymptotically, unstable. For each case considered, two predominant modes of transient amplification are identified: a predictable intra-period growth for translational capsule perturbations and period-to-period growth for certain capsule distortions. The amplitude of the intra-period growth depends linearly on the flow strength and oscillation period, which corresponds to a shift of the flow stagnation point, and the period-to-period growth saturates over several periods, commensurate with the asymptotic stability of the flow.Critical evolution of finite perturbations of a water evaporation surface in porous mediahttps://www.zbmath.org/1475.760452022-01-14T13:23:02.489162Z"Gorkunov, S. V."https://www.zbmath.org/authors/?q=ai:gorkunov.sergey-v"Il'ichev, A. T."https://www.zbmath.org/authors/?q=ai:ilichev.andrej-t"Shargatov, V. A."https://www.zbmath.org/authors/?q=ai:shargatov.v-aSummary: It is shown that the approximate steady-state solutions, which satisfy the model dissipative equation that describes the process of water evaporation in the neighborhood of the instability threshold of a phase transition interface, determine localized damped finite-amplitude perturbations when a certain condition is fulfilled. These steady-state solutions can be used for forecasting the scenario of the development of a perturbation with sufficient accuracy if this perturbation has no common points with any steady-state solution. If the initial position of the phase transition front is located between the spectrally stable solution and any of the steady-state solutions, this front damps. If the initial position of the front is located above at least one of the spectrally unstable steady-state solutions, then the solution is catastrophically restructured.The effects of surface tension on modulational instability in full-dispersion water-wave modelshttps://www.zbmath.org/1475.760462022-01-14T13:23:02.489162Z"Pandey, Ashish Kumar"https://www.zbmath.org/authors/?q=ai:pandey.ashish-kumarSummary: We study the modulational instability of a shallow water model, with and without surface tension, which generalizes the Whitham equation to include bi-directional propagation. Without surface tension, the small amplitude periodic traveling waves are modulationally unstable if their wave number is greater than a critical wave number predicting a Benjamin-Feir type instability and the result qualitatively agrees with the shallow water model in [\textit{V. M. Hur} and the author, Stud. Appl. Math. 142, No. 1, 3--47 (2019; Zbl 1420.35241)]. With surface tension, the result qualitatively agrees with the physical problem except for the large surface tension limit which is accurately predicted by the shallow water model in [loc. cit.]. We also compare the results with the Whitham and full-dispersion Camassa-Holm equations. We conclude that the shallow water model in Hur and Pandey [loc. cit.] is a better model than the shallow water model presented here when the effects of surface tension on modulational instability is considered.Instability of a light fluid over a heavy one under the motion of their interface in a porous mediumhttps://www.zbmath.org/1475.760472022-01-14T13:23:02.489162Z"Tsypkin, G. G."https://www.zbmath.org/authors/?q=ai:tsypkin.george-gSummary: The stability of the moving interface between a gas and a liquid in a porous medium is considered. The gas region is assumed to be located above the region saturated with liquid. The applications of the problem to the underground water flow through a porous medium and the motion of oil in an oil field with gas cap are considered. It is shown that the interface becomes unstable when underground water moves in the nonwettable medium and in the medium with a capillary pressure gradient, as well as in oil field operation when the reservoir pressure becomes lower than the gas-cap pressure. In the presence of the dissolved admixture such an instability can lead to soil salinization, while in oil field operation the instability can lead to formation of residual oil.On linear instability of atmospheric quasi-hydrostatic equations in response to small shortwave perturbationshttps://www.zbmath.org/1475.760482022-01-14T13:23:02.489162Z"Xu, X."https://www.zbmath.org/authors/?q=ai:xu.xinli|xu.xiaohua.1|xu.xueqiao|xu.xiaxia|xu.xuiling|xu.xing-guang|xu.xiaoxin|xu.xianjin|xu.xuxin|xu.xiangshen|xu.xiaolong|xu.xuczi|xu.xiangxiang|xu.xiaoning|xu.xinya|xu.xiujuan|xu.xuhai|xu.xuejun.1|xu.xinlong|xu.xiaoyi|xu.xingbo|xu.xianhao|xu.xinmin|xu.xuesong|xu.xiaochuan|xu.xiaoka|xu.xiangbin|xu.xinggen|xu.xinsheng|xu.xinpeng|xu.xhaoji|xu.xiaowen|xu.xueting|xu.xiaona|xu.xianzhen|xu.xianfan|xu.xianghui|xu.xiuzhen|xu.xiansheng|xu.xingdong|xu.xiaoquan|xu.xinying|xu.xiangjin|xu.xunlei|xu.xuhua|xu.xiaoxia|xu.xiaoyong|xu.xiangru|xu.xuemei|xu.xiubin|xu.xiaosu|xu.xiaolan|xu.xiaopeng|xu.xinyin|xu.xiaolei|xu.xiaoyan|xu.xindong|xu.xuemin|xu.xiaoxiao|xu.xing|xu.xiuhua|xu.xinwei|xu.xiaoman|xu.xinming|xu.xiaofu|xu.xiaoge|xu.xinzhong|xu.xuewen|xu.xiaolin|xu.xiaofang|xu.xinlin|xu.xi|xu.xiaohui|xu.xinjun|xu.xiaojuan|xu.xuan|xu.xueke|xu.xinping|xu.xiangkun|xu.xiangnan|xu.xiao|xu.xianzhi|xu.xihua|xu.xiumei|xu.xinzheng|xu.xiaohao|xu.xiaofeng|xu.xilei|xu.xiaoping.2|xu.xiangjian|xu.xusong|xu.xinhe|xu.xuequn|xu.xinhui|xu.xuebin|xu.xiangwei|xu.xingfu|xu.xiuwei|xu.xinzhe|xu.xiaochen|xu.xiaoyu|xu.xingchen|xu.xinxi|xu.xibin|xu.xiaoqing|xu.xiaodong|xu.xiaozeng|xu.xiaolu|xu.xaiojian|xu.xiaoya|xu.xiaoyang|xu.xingzhi|xu.xiaoshuang|xu.xinzhai|xu.xianliang|xu.xufeng|xu.xiqing|xu.xinzhou|xu.xuelian|xu.xushan|xu.xiaoshu|xu.xiaojun|xu.xiaoping.3|xu.xiurong|xu.xiaomeng|xu.xiaoqiang|xu.xiaohong|xu.xonglian|xu.xinwen|xu.xiaolai|xu.xiaoxiao.1|xu.xiaole|xu.xiaoling|xu.xuexin|xu.xiaobin|xu.xuelin|xu.xiwu|xu.xianyun|xu.xiaozhan|xu.xiuxiu|xu.xiaogang|xu.xudong|xu.xiaoguan|xu.xianfa|xu.xiaohu|xu.xinglei|xu.xiuling|xu.xiufang|xu.xiaochun|xu.xia|xu.ximing|xu.xiaodan|xu.xiangyu|xu.xinhai|xu.xuejun|xu.xiaoyun|xu.xiaorong|xu.xiong|xu.xunqian|xu.xianghong|xu.xiaojie|xu.xiaoqian|xu.xian|xu.xiaoping.1|xu.xiaoli|xu.xuefeng|xu.xuanxuan|xu.xianchun|xu.xinjian|xu.xin|xu.xun|xu.xiuyan|xu.xintong|xu.xuying|xu.xiaodi|xu.xigen|xu.xingwang|xu.xiaoliang|xu.xiaoying|xu.xue|xu.xingyi|xu.xianghua|xu.xiaozhong|xu.xinshan|xu.xingxin|xu.xiwen|xu.xiaochuan.1|xu.xianwei|xu.xinkuo|xu.xingkui|xu.xingjian|xu.xueguo|xu.xianqi|xu.xinzai|xu.xiangqin|xu.xuefen|xu.xiangjing|xu.xingcheng|xu.xuemiao|xu.xiaojing.1|xu.xiaoran|xu.xianglian|xu.xiaoduo|xu.xingliang|xu.xirong|xu.xianmin|xu.xiaomei|xu.xiaofei|xu.xingping|xu.xinshun|xu.xinxin|xu.xuping|xu.xinyu|xu.xiaoquan.1|xu.xueyou|xu.xiaoguang|xu.xiaoping|xu.xiuli|xu.xingye|xu.xiangming|xu.xiankun|xu.xiaoming|xu.xuming|xu.xie|xu.xuchang|xu.xuezi|xu.xihai|xu.xiu|xu.xiaomin|xu.xingzhong|xu.xianzhong|xu.xiaowei|xu.xiaonian|xu.xiangde|xu.xiangtian|xu.xiaowei.1|xu.xinxing|xu.xingyu|xu.xiaoxue|xu.xiaoting|xu.xiaoyin|xu.xuequan|xu.xixiang|xu.xiangyang|xu.xuanhua|xu.xiaobing|xu.xiaoxu|xu.xiangyuan|xu.xinlu|xu.xuexiang|xu.xiangwen|xu.xu.2|xu.xiaoxing|xu.xiangdong|xu.xueli|xu.xiaoxi|xu.xioaping|xu.xiaojian|xu.xingbai|xu.xinyi|xu.xiaoke|xu.xiangmin|xu.xiaozhu|xu.xiping|xu.xining|xu.xiufen|xu.xiaobo|xu.xiyang|xu.xiaotian|xu.xinliang|xu.xiaozhi|xu.xingyao|xu.xinyue|xu.xiaozhuo|xu.xiang|xu.xindi|xu.xieqing|xu.xueqin|xu.xiaoqin|xu.xianmin.1|xu.xulin|xu.xiaosong|xu.xiangping|xu.xu|xu.xiaofan|xu.xiangsheng|xu.xiaojing|xu.xuerong|xu.xiaotai|xu.xuebiao"Nigmatulin, R. I."https://www.zbmath.org/authors/?q=ai:nigmatulin.robert-iSummary: A set of 3-dimensional atmospheric-dynamics equations with quasi-hydrostatic approximation is proposed and justified with the practical goal to optimize atmospheric modelling at scales ranging from meso meteorology to global climate. Sound waves are filtered by applying the quasi-hydrostatic approximation. In the closed system of hydro/thermodynamic equations, the inertial forces are negligibly small compared to gravity forces, and the asymptotically exact equation for vertical velocity is obtained. Investigation of the stability of solutions to this system in response to small shortwave perturbations has shown that solutions have the property of shortwave instability. There are situations when the increment of the perturbation amplitude tends to infinity, corresponding to absolute instability. It means that the Cauchy problem for such equations may be ill-posed. Its formulation can become conditionally correct if solutions are sought in a limited class of sufficiently smooth functions whose Fourier harmonics tend to zero reasonably quickly when the wavelengths of the perturbations approach zero. Thus, the numerical scheme for the quasi-hydrostatic equations using the finite-difference method requires an adequately selected pseudo-viscosity to eliminate the instability caused by perturbations with wavelengths of the order of the grid size. The result is useful for choosing appropriate vertical and horizontal grid sizes for modelling to avoid shortwave instability associated with the property of the system of equations. Implementation of pseudo-viscosities helps to smoothen or suppress the perturbations that occur during modelling.Stability of Couette flow for 2D Boussinesq system in a uniform magnetic field with vertical dissipationhttps://www.zbmath.org/1475.760492022-01-14T13:23:02.489162Z"Bian, Dongfen"https://www.zbmath.org/authors/?q=ai:bian.dongfen"Dai, Shouyi"https://www.zbmath.org/authors/?q=ai:dai.shouyi"Mao, Jingjing"https://www.zbmath.org/authors/?q=ai:mao.jingjingSummary: In this paper, we establish the nonlinear stability of Couette flow in a uniform magnetic field for the Boussinesq equations with magnetohydrodynamics convection in the domain \(\mathbb{T} \times \mathbb{R}\) with only vertical dissipation. This extends the result for full dissipation case in the reference [the first author and \textit{X. Pu}, J. Math. Fluid Mech. 22, No. 1, Paper No. 12, 13 p. (2020; Zbl 1433.35258)] to partial dissipation case and the result for Boussinesq system in the reference [\textit{W. Deng} et al., J. Funct. Anal. 281, No. 12, Article ID 109255, 40 p. (2021; Zbl 07412900)] to the full system in the presence of the magnetic field.Long time behavior of Alfvén waves in flowing plasma: the destruction of the magnetic islandhttps://www.zbmath.org/1475.760502022-01-14T13:23:02.489162Z"Ren, Siqi"https://www.zbmath.org/authors/?q=ai:ren.siqi"Wei, Dongyi"https://www.zbmath.org/authors/?q=ai:wei.dongyi"Zhang, Zhifei"https://www.zbmath.org/authors/?q=ai:zhang.zhifeiNew instability of a thin vortex ring in an ideal fluidhttps://www.zbmath.org/1475.760512022-01-14T13:23:02.489162Z"Akinshin, R. V."https://www.zbmath.org/authors/?q=ai:akinshin.r-vSummary: The problem of stability of steady-state thin vortex ring flow in an ideal fluid is studied in the linear approximation. The case of the isochronous vortex ring in which the liquid-particle rotation periods are identical is considered. In such a flow there are no perturbations of the continuous spectrum. This makes considerably easier to solve this complex problem. The instability of longwave oscillations related to the interaction between the perturbations with energy of different signs, namely, the oscillations with positive and negative energy, is revealed.Features of laminar-turbulent transition for the coolant flow in a plane heat-exchanger channelhttps://www.zbmath.org/1475.760522022-01-14T13:23:02.489162Z"Nizamova, A. D."https://www.zbmath.org/authors/?q=ai:nizamova.a-d"Murtazina, R. D."https://www.zbmath.org/authors/?q=ai:murtazina.r-d"Kireev, V. N."https://www.zbmath.org/authors/?q=ai:kireev.victor-n"Urmancheev, S. F."https://www.zbmath.org/authors/?q=ai:urmancheev.s-fSummary: The presented work is devoted to one problem of hydrodynamic stability of a thermoviscous fluid. The stability of the flow of a 45\% aqueous solution of propylene glycol in a plane channel with a linear temperature distribution was considered. The solution of the obtained generalized Orr-Sommerfeld equation was carried out using the spectral method of expanding the sought functions in terms of the first kind Chebyshev polynomials. As a result of calculations, the distributions of eigenvalues were constructed for different parts of the curve of the dependence of viscosity on the temperature of the liquid under consideration, in each case the critical Reynolds numbers and eigenfunctions were determined. It was found that taking into account the dependence of the viscosity on the temperature of the liquid leads to an increase in the region of unstable flow regimes in the channels of heat exchangers.A reverse transition route from inertial to elasticity-dominated turbulence in viscoelastic Taylor-Couette flowhttps://www.zbmath.org/1475.760532022-01-14T13:23:02.489162Z"Song, Jiaxing"https://www.zbmath.org/authors/?q=ai:song.jiaxing"Wan, Zhen-Hua"https://www.zbmath.org/authors/?q=ai:wan.zhenhua.1"Liu, Nansheng"https://www.zbmath.org/authors/?q=ai:liu.nansheng"Lu, Xi-Yun"https://www.zbmath.org/authors/?q=ai:lu.xiyun"Khomami, Bamin"https://www.zbmath.org/authors/?q=ai:khomami.baminSummary: A high-order transition route from inertial to elasticity-dominated turbulence (EDT) in Taylor-Couette flows of polymeric solutions has been discovered via direct numerical simulations. This novel two-step transition route is realized by enhancing the extensional viscosity and hoop stresses of the polymeric solution via increasing the maximum chain extension at a fixed polymer concentration. Specifically, in the first step inertial turbulence is stabilized to a laminar flow much like the modulated wavy vortex flow. The second step destabilizes this laminar flow state to EDT, i.e. a spatially smooth and temporally random flow with a \(-3.5\) scaling law of the energy spectrum reminiscent of elastic turbulence. The flow states involved are distinctly different to those observed in the reverse transition route from inertial turbulence via a relaminarization of the flow to elasto-inertial turbulence in parallel shear flows, underscoring the importance of polymer-induced hoop stresses in realizing EDT that are absent in parallel shear flows.Resolvent-based estimation of turbulent channel flow using wall measurementshttps://www.zbmath.org/1475.760542022-01-14T13:23:02.489162Z"Amaral, Filipe R."https://www.zbmath.org/authors/?q=ai:amaral.filipe-r"Cavalieri, André V. G."https://www.zbmath.org/authors/?q=ai:cavalieri.andre-v-g"Martini, Eduardo"https://www.zbmath.org/authors/?q=ai:martini.eduardo"Jordan, Peter"https://www.zbmath.org/authors/?q=ai:jordan.peter"Towne, Aaron"https://www.zbmath.org/authors/?q=ai:towne.aaronSummary: We employ a resolvent-based methodology to estimate velocity and pressure fluctuations within turbulent channel flows at friction Reynolds numbers of approximately 180, 550 and 1000 using measurements of shear stress and pressure at the walls, taken from direct numerical simulation (DNS) databases. The third author et al. [J. Fluid Mech. 900, Paper No. A2, 38 p. (2020; Zbl 1460.76569), p. A2] showed that the resolvent-based estimator is optimal when the true space-time forcing statistics are utilised, thus providing an upper bound for the accuracy of any linear estimator. We use this framework to determine the flow structures that can be linearly estimated from wall measurements, and we characterise these structures and the estimation errors in both physical and wavenumber space. We also compare these results to those obtained using approximate forcing models -- an eddy-viscosity model and white-noise forcing -- and demonstrate the significant benefit of using true forcing statistics. All models lead to accurate results up to the buffer layer, but only using the true forcing statistics allows accurate estimation of large-scale logarithmic-layer structures, with significant correlation between the estimates and DNS results throughout the channel. The eddy-viscosity model displays an intermediate behaviour, which may be related to its ability to partially capture the forcing colour. Our results show that structures that leave a footprint on the channel walls can be accurately estimated using the linear resolvent-based methodology, and the presence of large-scale wall-attached structures enables accurate estimations through the logarithmic layer.Some reasons for nonmonotonic variation of discrete-phase concentration in a turbulent two-phase jethttps://www.zbmath.org/1475.760552022-01-14T13:23:02.489162Z"Zuev, Yu. V."https://www.zbmath.org/authors/?q=ai:zuev.yu-vSummary: A mathematical model of a two-phase turbulent jet flow is presented, the averaged equations of which are written for each phase in Euler variables. Analysis of the results of calculations performed using this mathematical model made it possible to identify the origins of a nonmonotonic variation in the volume concentration of the dispersed phase along the axis of the two-phase jet. The influence of particle size, transverse velocity, particle concentration, and phase velocity slip in the initial section of the jet on the variation of the particle concentration in the jet is considered. It is shown that the listed factors cause a nonmonotonic variation in the particle volume concentration in a two-phase jet only when the value of the Stokes number based on the phase parameters in the initial section of the jet is greater than 0.14-0.15. At lower values of the Stokes number, when the particles can be regarded as a passive admixture, their volume fraction in the jet decreases monotonically along the jet axis, same as the impurity concentration in a gas jet of variable composition.Theoretical study of Mach number and compressibility effect on the slender airfoilshttps://www.zbmath.org/1475.760562022-01-14T13:23:02.489162Z"Hoque, Abrar"https://www.zbmath.org/authors/?q=ai:hoque.abrar"Rahman, Masudar"https://www.zbmath.org/authors/?q=ai:rahman.masudar"Hoque, Ashabul"https://www.zbmath.org/authors/?q=ai:hoque.ashabulSummary: Theoretical development of the velocity potential equation for compressible flow and its various consequences has been presented. The geometrical interpretation of potential equation and conformal mapping technique are discussed where the mappings link the flow around a circular cylinder of a slender airfoil. The lift and drag coefficients are determined for the slender airfoils based on the Mach number and compressibility effects. The calculated lift coefficients show that with the increasing of attack angle it increases linearly and a higher lift coefficient is found for a smaller Mach number for any certain attack angle. Similarly, the drag profiles are determined which are exponentially decreased with the increasing of Mach number for any fixed attack angle. The calculated and experimental data on the lift and drag coefficients over the slender airfoil surface are compared and found in good agreement.Gas effect for oblique and conical shock waves at high temperaturehttps://www.zbmath.org/1475.760572022-01-14T13:23:02.489162Z"Yahiaoui, Toufik"https://www.zbmath.org/authors/?q=ai:yahiaoui.toufik"Zebbiche, Toufik"https://www.zbmath.org/authors/?q=ai:zebbiche.toufik"Allali, Abderrazak"https://www.zbmath.org/authors/?q=ai:allali.abderrazak"Boun-Jad, Mohamed"https://www.zbmath.org/authors/?q=ai:boun-jad.mohamedSummary: The work focuses to develop a new numerical calculation program for determining the gas effect at high temperature instead air on the calculation of the oblique and conical shock waves parameters and make applications for various external and internal aerodynamics problems like, the calculation of the suitable intake adaptation parameters, dihedron and cone wave drag, aerodynamic coefficients of a pointed supersonic airfoil and oblique shock reflection without forgetting others no less important like the detonation propulsion and the dust explosion applications, where the high temperature gas effect is very important. All this for future aerodynamics (gas dynamics) like the phenomenon of climate change in the near and far future because of the enlargement progressive of the layer ozone hole which will lead to an increase in the temperature of the ambient medium, and by the environment pollution by the shining of the waste which will cause a new decomposition of gases from the ambient environment. Another interesting application for actual aerodynamics (gas dynamics) is the performance of tests in wind tunnels supplied by a combustion chamber making a reaction of gases giving a gas with new thermodynamics parameters which is not necessarily air. To make a calculation, the selected gases are \(H_2, O_2, N_2\), CO, \(CO_2, H_2\) O, \(NH_3, CH_4\) and air. All shock parameters depend on the stagnation temperature, upstream Mach number, the thermodynamics of the used gas, dihedron and cone deviation and others parameters. The specific heat at constant pressure varies with the temperature and the selected gas. Gas is still considered as perfect. It is calorically imperfect, and thermally perfect, less than the molecules dissociation threshold. A comparison between the parameters of each gas and air is presented to choose the suitable gas witch giving good performances as required by design parameters instead air.Scalable domain decomposition algorithms for simulation of flows passing full size wind turbinehttps://www.zbmath.org/1475.760582022-01-14T13:23:02.489162Z"Chen, Rongliang"https://www.zbmath.org/authors/?q=ai:chen.rongliang"Yan, Zhengzheng"https://www.zbmath.org/authors/?q=ai:yan.zhengzheng"Zhao, Yubo"https://www.zbmath.org/authors/?q=ai:zhao.yubo"Cai, Xiao-Chuan"https://www.zbmath.org/authors/?q=ai:cai.xiao-chuanSummary: Accurate numerical simulation of fluid flows around wind turbine plays an important role in understanding the performance and also the design of the wind turbine. The computation is challenging because of the large size of the blades, the large computational mesh, the moving geometry, and the high Reynolds number. In this paper, we develop a highly parallel numerical algorithm for the simulation of fluid flows passing three-dimensional full size wind turbine including the rotor, nacelle, and tower with realistic geometry and Reynolds number. The flow in the moving domain is modeled by unsteady incompressible Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form and a non-overlapping sliding-interface method is used to handle the relative motion of the rotor and the tower. A stabilized moving mesh finite element method is introduced to discretize the problem in space, and a fully implicit scheme is used to discretize the temporal variable. A parallel Newton-Krylov method with a new domain decomposition type preconditioner, which combines a non-overlapping method across the rotating interface and an overlapping Schwarz method in the remaining subdomains, is applied to solve the fully coupled nonlinear algebraic system at each time step. To understand the efficiency of the algorithm, we test the algorithm on a supercomputer for the simulation of a realistic 5MW wind turbine. The numerical results show that the newly developed algorithm is scalable with over 8000 processor cores for problems with tens of millions of unknowns.An XFEM implementation of a projection method for 3D incompressible two-fluid flows with arbitrary high contrasts in material propertieshttps://www.zbmath.org/1475.760592022-01-14T13:23:02.489162Z"Garajeu, Daniela"https://www.zbmath.org/authors/?q=ai:garajeu.daniela"Medale, Marc"https://www.zbmath.org/authors/?q=ai:medale.marcSummary: This paper presents an \textit{XFEM} implementation of a projection algorithm to compute in an Eulerian framework 3D incompressible two-fluid flows with arbitrary high contrasts in material properties. It is designed to deal with both strong and weak discontinuities across the interface for pressure and velocity fields, respectively. A classical enrichment function accounts for velocity gradient discontinuities across the interface and a new quadratic enrichment function accounts for pressure discontinuities across the interface. A splitting of two-fluid elements is performed to achieve accurate numerical integrations, meanwhile a scaling coefficient accounting for both physical and geometrical considerations alleviates ill-conditioning. Various validations have been carried and very good solution accuracy is achieved even on coarse meshes, as from the minimal mesh not conforming to the interface. This implementation enables to compute accurate solutions regardless of discontinuity magnitude (arbitrary high contrast in material properties) and mesh size of two-fluid elements, which can constitute a decisive advantage for large size 3D computations.A three-field smoothed formulation for prediction of large-displacement fluid-structure interaction via the explicit relaxed interface coupling (ERIC) schemehttps://www.zbmath.org/1475.760602022-01-14T13:23:02.489162Z"He, Tao"https://www.zbmath.org/authors/?q=ai:he.taoSummary: A three-field smoothed formulation is proposed in this paper for the resolution of fluid-structure interaction (FSI) from the arbitrary Lagrangian-Eulerian perspective. The idea behind the proposed approach lies in different smoothing concepts. Both fluid and solid stress tensors are smoothly treated by the cell-based smoothed finite element method (CS-FEM) using four-node quadrilateral elements. In particular, the smoothed characteristic-based split technique is developed for the incompressible flows whereas the geometrically nonlinear solid is settled through CS-FEM as usual. The deformable mesh, often represented by a pseudo-structural system, is further tuned with the aid of a hybrid smoothing algorithm. The Explicit Relaxed Interface Coupling (ERIC) scheme is presented to interpret the nonlinear FSI effect, where all interacting fields are explicitly coupled in alliance with interface relaxation method for numerical stability. The promising ERIC solver is in detail validated against the previously published data for a large-displacement FSI benchmark. The good agreement is revealed in computed results and well-known flow-induced phenomena are accurately captured.Discontinuous Galerkin model order reduction of geometrically parametrized Stokes equationhttps://www.zbmath.org/1475.760612022-01-14T13:23:02.489162Z"Shah, Nirav Vasant"https://www.zbmath.org/authors/?q=ai:shah.nirav-vasant"Hess, Martin Wilfried"https://www.zbmath.org/authors/?q=ai:hess.martin-wilfried"Rozza, Gianluigi"https://www.zbmath.org/authors/?q=ai:rozza.gianluigiSummary: The present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order model is based on the discontinuous Galerkin method with an interior penalty formulation. We introduce the broken Sobolev spaces as well as the weak formulation required for an affine parameter dependency. The operators are transformed from a fixed domain to a parameter dependent domain using the affine parameter dependency. The proper orthogonal decomposition is used to obtain the basis of functions of the reduced order model. By using the Galerkin projection the linear system is projected onto the reduced space. During this process, the offline-online decomposition is used to separate parameter dependent operations from parameter independent operations. Finally this technique is applied to an obstacle test problem. The numerical outcomes presented include experimental error analysis, eigenvalue decay and measurement of online simulation time.
For the entire collection see [Zbl 1471.65009].Numerical simulation and benchmarking of drops and bubbleshttps://www.zbmath.org/1475.760622022-01-14T13:23:02.489162Z"Turek, Stefan"https://www.zbmath.org/authors/?q=ai:turek.stefan"Mierka, Otto"https://www.zbmath.org/authors/?q=ai:mierka.ottoSummary: The numerical simulation of immiscible multiphase flow problems, particularly including drops and bubbles, is very important in many applications, and performing accurate, robust and efficient numerical computations has been the object of numerous research and simulation projects for many years. One of the main challenges for the underlying numerical methods -- besides the fact that the computational simulation of the incompressible Navier-Stokes equations is challenging by itself -- is that the position of the moving interface between two fluids is unknown and must be determined as part of the boundary value problem to be solved. In this contribution, we provide a compact description of state-of-the-art numerical solvers for such multiphase flow problems, namely interface tracking and interface capturing methods. It is demonstrated that corresponding discretization and solution approaches which are based on Finite Element and Discrete Projection methods for the Navier-Stokes equations, combined with corresponding numerical tools for both interface capturing, resp., tracking approaches, lead to robust, accurate, flexible, and efficient simulation tools. Moreover, we present several numerical test cases of benchmarking type which first of all shall help to evaluate the quality of the underlying flow solvers. In particular, we describe the settings for a quantitative 3D Rising Bubble benchmark which can be used for `simple' validation and evaluation of multiphase CFD codes without the necessity of complex postprocessing operations. Finally, we also provide numerical reference values for a `Taylor bubble' setting, and we show simulation results of a reactive Taylor bubble flow in the framework of estimating reaction parameters to match corresponding experimentally obtained results. All reference benchmark quantities can be downloaded from www.featflow.de.
For the entire collection see [Zbl 1458.35003].An improved immersed boundary method with new forcing point searching scheme for simulation of bodies in free surface flowshttps://www.zbmath.org/1475.760632022-01-14T13:23:02.489162Z"Yan, Bin"https://www.zbmath.org/authors/?q=ai:yan.bin"Bai, Wei"https://www.zbmath.org/authors/?q=ai:bai.wei"Quek, Ser Tong"https://www.zbmath.org/authors/?q=ai:quek.ser-tongSummary: An improved immersed boundary method is proposed and applied to simulate fluid-structure interactions by combining a level set method for free water surface capturing. An efficient Navier-Stokes equation solver adopting the fractional step method at a staggered Cartesian grid system is used to solve the incompressible fluid motion. A new efficient algorithm to search forcing points near the immersed body boundary is developed. The searching schemes for forcing points located both inside and outside the solid phase with the linear interpolation schemes for the determination of velocities at forcing points are presented and compared via the case of dam break over obstacles. The accuracy and effectiveness of the proposed forcing point searching schemes are further demonstrated by the study of wave propagation over a submerged bar and more challenging cases of wedge with prescribed velocity or falling freely into the water. By the extensive comparison of present numerical results with other experimental and numerical data, it suggests that the present improved immersed boundary method with the new forcing point searching scheme has a better performance and is very promising due to its accuracy, efficiency and ease of implementation. Furthermore, the present numerical results show that the outside forcing scheme is superior over the inside forcing scheme.Parallel iterative stabilized finite element methods based on the quadratic equal-order elements for incompressible flowshttps://www.zbmath.org/1475.760642022-01-14T13:23:02.489162Z"Zheng, Bo"https://www.zbmath.org/authors/?q=ai:zheng.bo|zheng.bo.1"Shang, Yueqiang"https://www.zbmath.org/authors/?q=ai:shang.yueqiangAuthors' abstract: Combining the quadratic equal-order stabilized method with the approach of local and parallel finite element computations and classical iterative methods for the discretization of the steady-state Navier-Stokes equations, three parallel iterative stabilized finite element methods based on fully overlapping domain decomposition are proposed and compared in this paper. In these methods, each processor independently computes an approximate solution in its own subdomain using a global composite mesh that is fine around its own subdomain and coarse elsewhere, making the methods be easy to implement based on existing codes and have low communication complexity. Under some (strong) uniqueness conditions, stability and convergence theory of the parallel iterative stabilized methods are derived. Numerical tests are also performed to demonstrate the stability, convergence orders and high efficiency of the proposed methods.
Reviewer: Dimitra Antonopoulou (Chester)Application of the GRP scheme for cylindrical compressible fluid flowshttps://www.zbmath.org/1475.760652022-01-14T13:23:02.489162Z"Chen, Rui"https://www.zbmath.org/authors/?q=ai:chen.rui"Li, Jiequan"https://www.zbmath.org/authors/?q=ai:li.jiequan"Tian, Baolin"https://www.zbmath.org/authors/?q=ai:tian.baolinSummary: This paper contributes to apply both the direct Eulerian and Lagrangian generalized Riemann problem (GRP) schemes for the simulation of compressible fluid flows in two-dimensional cylindrical geometry. Particular attention is paid to the treatment of numerical boundary conditions at the symmetric center besides the zero velocity (momentum) enforced by the symmetry. The new treatment precisely describes how the thermodynamical variables are discretized near the center using the conservation property. Moreover, the Lagrangian GRP scheme is verified rigorously to satisfy the properties of symmetry and conservation. Numerical results demonstrate the performance of such treatments and the symmetry preserving property of the scheme with second order accuracy both in space and time.A direct ALE multi-moment finite volume scheme for the compressible Euler equationshttps://www.zbmath.org/1475.760662022-01-14T13:23:02.489162Z"Jin, Peng"https://www.zbmath.org/authors/?q=ai:jin.peng"Deng, Xi"https://www.zbmath.org/authors/?q=ai:deng.xi"Xiao, Feng"https://www.zbmath.org/authors/?q=ai:xiao.fengSummary: A direct Arbitrary Lagrangian Eulerian (ALE) method based on multi-moment finite volume scheme is developed for the Euler equations of compressible gas in 1D and 2D space. Both the volume integrated average (VIA) and the point values (PV) at cell vertices, which are used for high-order reconstructions, are treated as the computational variables and updated simultaneously by numerical formulations in integral and differential forms respectively. The VIAs of the conservative variables are solved by a finite volume method in the integral form of the governing equations to ensure the numerical conservativeness; whereas, the governing equations of differential form are solved for the PVs of the primitive variables to avoid the additional source terms generated from moving mesh, which largely simplifies the solution procedure. Numerical tests in both 1D and 2D are presented to demonstrate the performance of the proposed ALE scheme. The present multi-moment finite volume formulation consistent with moving meshes provides a high-order and efficient ALE computational model for compressible flows.A high-resolution cell-centered Lagrangian method with a vorticity-based adaptive nodal solver for two-dimensional compressible Euler equationshttps://www.zbmath.org/1475.760672022-01-14T13:23:02.489162Z"Qi, Jin"https://www.zbmath.org/authors/?q=ai:qi.jin"Tian, Baolin"https://www.zbmath.org/authors/?q=ai:tian.baolin"Li, Jiequan"https://www.zbmath.org/authors/?q=ai:li.jiequanSummary: In this work, a second-order high-resolution LAgrangian method with a Vorticity-based Adaptive Nodal Solver (LAVANS) is proposed to overcome the numerical difficulty of traditional Lagrangian methods for the simulation of multidimensional flows. The work mainly include three aspects to improve the performance of the traditional CAVEAT-type cell-centered Lagrangian method. First, a vorticity-based adaptive least-squares method for vertex velocity computation is proposed to suppress nonphysical mesh distortion caused by the traditional five-point-stencil least-squares method. Second, a simple interface flux modification is proposed such that the geometry conservation law is satisfied. Third, a generalized Riemann problem solver is employed in the LAVANS scheme to achieve one-step time-space second-order accuracy. Some typical benchmark numerical tests validate the performance of the LAVANS scheme.Incorporation of NURBS boundary representation with an unstructured finite volume approximationhttps://www.zbmath.org/1475.760682022-01-14T13:23:02.489162Z"Xia, Yifan"https://www.zbmath.org/authors/?q=ai:xia.yifan"Wang, Gaofeng"https://www.zbmath.org/authors/?q=ai:wang.gaofeng"Zheng, Yao"https://www.zbmath.org/authors/?q=ai:zheng.yao"Ji, Tingwei"https://www.zbmath.org/authors/?q=ai:ji.tingwei"Loh, Ching Y."https://www.zbmath.org/authors/?q=ai:loh.ching-yuenSummary: For compressible flow computations, the present paper extends the ETAU (enhanced time-accurate upwind) unstructured finite volume (FV) scheme to handle curved domain boundary with better accuracy. For the interior cells in the computational domain or the boundary cells with straight line boundary, the original ETAU scheme with second order accuracy in space and time is applied. For those boundary cells with the curved geometry, a more accurate Non-Uniform Rational B-Spline (NURBS) representation of the boundary is considered. The NURBS is commonly employed in computer aided design (CAD) to construct complex geometries. Here, it yields an exact geometry expression of complex boundary geometry. By combining ETAU with NURBS, the NURBS incorporated ETAU scheme (NETAU) is proposed for more accurate geometrical representation and fluxes evaluation. Details of the computing procedure of the geometry and surface fluxes for cells on the curved boundary, such as special transformation strategies and merging of ETAU and NURBS, are introduced and implemented. With NURBS, the NETAU scheme are geometrically versatile and more flexible. Several two-dimensional (2D) numerical cases are investigated to demonstrate the performance, computing efficiency and benefits of the NETAU scheme. The numerical results show that, for flows with low speed and high Reynolds number, the NETAU scheme provides more accurate pressure distribution on curved boundary than the original ETAU scheme. Meanwhile, the high-speed flow case shows that the NETAU scheme is still stable for high Mach number problem with shocks. Thus, the NETAU scheme potentially provides an accurate tool to describe complex geometry in computational fluid dynamics (CFD) simulations. It will help to reduce computational costs and enhances accuracy for flow domain dominated by complex geometries, with features such as high curvature and sharp edges.Conservative difference schemes for one-dimensional flows of polytropic gashttps://www.zbmath.org/1475.760692022-01-14T13:23:02.489162Z"Kozlov, Roman"https://www.zbmath.org/authors/?q=ai:kozlov.romanSummary: The paper considers one-dimensional flows of polytropic (calorically ideal) gas. These flows include three cases of gas dynamics: plain one-dimensional flows (one-dimensional space), radially symmetric flows in two-dimensional space and spherically symmetric flows in three-dimensional space. Starting with the difference schemes which have conservation laws of mass and energy (as well as conservation of momentum and the center of mass motion for the plain one-dimensional flows), we find difference schemes which also have additional conservation laws for the special values of the adiabatic exponent \(\gamma=1+2/d\), where \(d\) is the space dimension.For the stability of homogeneous explicit finite-difference scheme of two-dimensional non-steady flow of compressible viscid gas with microstructurehttps://www.zbmath.org/1475.760702022-01-14T13:23:02.489162Z"Verveiko, N. D."https://www.zbmath.org/authors/?q=ai:verveiko.nikolai-dmitrievich"Prosvetov, V. I."https://www.zbmath.org/authors/?q=ai:prosvetov.v-iSummary: This paper considers mathematical model of two-dimensional non-steady flow of compressible viscid gas with microstructure, its homogeneous explicit finite-difference scheme. Especially it was studied stability of finite-difference scheme subject to microstructure. It is obtained stability rating of geometric interval and time step under the condition, that dissipative term is added, when kinematic viscosity misses.Symmetries and differential invariants for inviscid flows on a curvehttps://www.zbmath.org/1475.760712022-01-14T13:23:02.489162Z"Duyunova, A."https://www.zbmath.org/authors/?q=ai:duyunova.anna-andreevna"Lychagin, V."https://www.zbmath.org/authors/?q=ai:lychagin.valentin-v"Tychkov, S."https://www.zbmath.org/authors/?q=ai:tychkov.sergey-nIn the paper under review, the focus is on inviscid flows on an oriented Riemannian manifold in the case when the manifold under consideration is a curve in the three-dimensional Euclidean space. Thus, one studies symmetry Lie algebras of the corresponding Euler system and their dependence on thermodynamic states.
Reviewer: Daniel Beltiţă (Bucureşti)Stationary flow predictions using convolutional neural networkshttps://www.zbmath.org/1475.760722022-01-14T13:23:02.489162Z"Eichinger, Matthias"https://www.zbmath.org/authors/?q=ai:eichinger.matthias"Heinlein, Alexander"https://www.zbmath.org/authors/?q=ai:heinlein.alexander"Klawonn, Axel"https://www.zbmath.org/authors/?q=ai:klawonn.axelSummary: Computational Fluid Dynamics (CFD) simulations are a numerical tool to model and analyze the behavior of fluid flow. However, accurate simulations are generally very costly because they require high grid resolutions. In this paper, an alternative approach for computing flow predictions using Convolutional Neural Networks (CNNs) is described; in particular, a classical CNN as well as the U-Net architecture are used. First, the networks are trained in an expensive offline phase using flow fields computed by CFD simulations. Afterwards, the evaluation of the trained neural networks is very cheap. Here, the focus is on the dependence of the stationary flow in a channel on variations of the shape and the location of an obstacle. CNNs perform very well on validation data, where the averaged error for the best networks is below 3\%. In addition to that, they also generalize very well to new data, with an averaged error below 10\%.
For the entire collection see [Zbl 1471.65009].A fully space-time least-squares method for the unsteady Navier-Stokes systemhttps://www.zbmath.org/1475.760732022-01-14T13:23:02.489162Z"Lemoine, Jérôme"https://www.zbmath.org/authors/?q=ai:lemoine.jerome"Münch, Arnaud"https://www.zbmath.org/authors/?q=ai:munch.arnaudSummary: We introduce and analyze a space-time least-squares method associated with the unsteady Navier-Stokes system. Weak solution in the two dimensional case and regular solution in the three dimensional case are considered. From any initial guess, we construct a minimizing sequence for the least-squares functional which converges strongly to a solution of the Navier-Stokes system. After a finite number of iterations related to the value of the viscosity coefficient, the convergence is quadratic. Numerical experiments within the two dimensional case support our analysis. This globally convergent least-squares approach is related to the damped Newton method.A hybrid moment method for multi-scale kinetic equations based on maximum entropy principlehttps://www.zbmath.org/1475.760742022-01-14T13:23:02.489162Z"Li, Weiming"https://www.zbmath.org/authors/?q=ai:li.weiming"Song, Peng"https://www.zbmath.org/authors/?q=ai:song.peng"Wang, Yanli"https://www.zbmath.org/authors/?q=ai:wang.yanliSummary: We propose a hybrid method for the multi-scale kinetic equations in the framework of the hyperbolic moment method [\textit{Z. Cai} and \textit{R. Li}, SIAM J. Sci. Comput. 32, No. 5, 2875--2907 (2010; Zbl 1417.82026)]. In this method, the fourth order moment system is chosen as the governing equations in the fluid region, while the hyperbolic moment system with arbitrary order is chosen as the governing equations in the kinetic region. When transiting from the fluid regime to the kinetic regime, the maximum entropy principle is adopted to reconstruct the kinetic distribution function, so that the information in the fluid region can be utilized thoroughly. Moreover, only one uniform set of numerical scheme is needed for both the fluid and kinetic regions. Numerical tests validate this new hybrid method.Data-driven, physics-based feature extraction from fluid flow fields using convolutional neural networkshttps://www.zbmath.org/1475.760752022-01-14T13:23:02.489162Z"Michelén Ströfer, Carlos"https://www.zbmath.org/authors/?q=ai:michelen-strofer.carlos-a"Wu, Jin-Long"https://www.zbmath.org/authors/?q=ai:wu.jinlong"Xiao, Heng"https://www.zbmath.org/authors/?q=ai:xiao.heng"Paterson, Eric"https://www.zbmath.org/authors/?q=ai:paterson.eric-gSummary: Feature identification is an important task in many fluid dynamics applications and diverse methods have been developed for this purpose. These methods are based on a physical understanding of the underlying behavior of the flow in the vicinity of the feature. Particularly, they require the definition of suitable criteria (i.e. point-based or neighborhood-based derived properties) and proper selection of thresholds. However, these methods rely on creative visualization of physical idiosyncrasies of specific features and flow regimes, making them non-universal and requiring significant effort to develop. Here we present a physics-based, data-driven method capable of identifying any flow feature it is trained to. We use convolutional neural networks, a machine learning approach developed for image recognition, and adapt it to the problem of identifying flow features. This provides a general method and removes the large burden placed on identifying new features. The method was tested using mean flow fields from numerical simulations, where the recirculation region and boundary layer were identified in several two-dimensional flows through a convergent-divergent channel, and the horseshoe vortex was identified in three-dimensional flow over a wing-body junction.A revisit of Navier-Stokes equationhttps://www.zbmath.org/1475.760762022-01-14T13:23:02.489162Z"Sheng, Wanan"https://www.zbmath.org/authors/?q=ai:sheng.wananThe authors studies the assumptions that serve as the base to derive the Navier-Stokes equation, focusing on the stress tensor and its symmetry. Along the history of the equation, its success, and challenges it is facing, the classical derivation is traced. Then the viscous stress tensor and surface forces are discussed for better understanding of the tensor and its components. The point is to separate the friction from the stress components, making it a special surface force. Several inconsistencies of the equation are described and asymmetric stress tensor is proposed. The equation is derived from the new assumptions, both for incompressible and compressible case: in the latter case, with modified assumptions compared to the classical ones. The author hopes that deriving the same equation from a more physical background would be of use.
Reviewer: Ilya A. Chernov (Petrozavodsk)Boundary-domain integral equation systems to the mixed BVP for compressible Stokes equations with variable viscosity in 2Dhttps://www.zbmath.org/1475.760772022-01-14T13:23:02.489162Z"Ayele, Tsegaye G."https://www.zbmath.org/authors/?q=ai:ayele.tsegaye-g"Dagnaw, Mulugeta A."https://www.zbmath.org/authors/?q=ai:dagnaw.mulugeta-aThe authors deal with the stationary Stokes problem in two dimensions with mixed boundary conditions. In particular, let \(\Omega\subset \mathbb R^2\) be a simply connected domain with infinitely smooth boundary. The problem in question is of the form
\[
\begin{aligned}
- \operatorname{div} (\mu D^d v) + \nabla p & = f\ \text{in }\Omega,\\
\operatorname{div} v & = g\ \text{in }\Omega,\\
v{\restriction}_{\partial \Omega_D} & = \varphi,\\
(\mu D^d v - \nabla p){\restriction}_{\partial \Omega_N} & = \psi,
\end{aligned}
\]
where \(v\) and \(p\) are unknowns, \(\mu\), \(f\), \(g\), \(\varphi\) and \(\psi\) are given functions of spatial variable \(x\) and \(D^d v = \nabla v + (\nabla v)^T -\alpha \operatorname{div} v\), where \(\alpha = 1\) or \(\alpha = \frac 23\).
In order to analyze the system, the authors present the relevant boundary-domain integral equations (BDIE) and they show the equivalence between the Stokes system and the BDIE. They introduce conditions which ensure the invertibility of corresponding boundary-layer potentials in the appropriate Bessel potential spaces and, in turn, also the unique solvability of the boundary-domain integral equations.
Reviewer: Václav Mácha (Praha)On exact analytical solutions of gas dynamic equationshttps://www.zbmath.org/1475.760782022-01-14T13:23:02.489162Z"Golubyatnikov, A. N."https://www.zbmath.org/authors/?q=ai:golubyatnikov.aleksandr-nikolaevich"Ukrainskii, D. V."https://www.zbmath.org/authors/?q=ai:ukrainskii.d-vSummary: The theory of construction of exact analytical solutions of the Cauchy problem using the power series depending on a special time variable whose form determines the particular class of motion is developed within one-dimensional time-dependent gas dynamics. Generally, the recurrent relations to the coefficients are finite and arranged so that there is no need to solve differential equations or integrate for calculation of the unknown functions and all the terms of series are determined successively from the initial conditions using only the algebraic operations and differentiation. This fact makes it possible also to find the terms of series exactly using any mathematical software package which admits of symbolic transformations. The necessary boundary conditions are discussed and the control techniques for the behavior of series are outlined. Some examples of the physical problems solved with the use of the method proposed are examined.Non-similar solutions of the boundary layers equations with favorable and adverse pressure gradients, isothermal wall and slip boundary conditions: application to Falkner-Skan gaseous flowhttps://www.zbmath.org/1475.760792022-01-14T13:23:02.489162Z"Essaghir, Elhoucine"https://www.zbmath.org/authors/?q=ai:essaghir.elhoucine"Oubarra, Abdelaziz"https://www.zbmath.org/authors/?q=ai:oubarra.abdelaziz"Lahjomri, Jawad"https://www.zbmath.org/authors/?q=ai:lahjomri.jawadSummary: This article presents the non-similar solutions of the steady incompressible two-dimensional boundary layers equations of momentum and energy for Falkner-Skan gaseous flow with favorable and adverse pressure gradient under slip boundary conditions at a relatively low Mach number. By considering the slip boundary conditions at the fluid-wall interface for the velocity and temperature, the non-dimensional boundary layer equations are solved numerically by using the centered implicit finite difference Keller Box methods. The results of the effects of different dimensionless parameters involved in the problem, namely the modified boundary layer Knudsen number, i.e., the slip parameter \(K\) and the shape parameter \(\beta\) on the local hydrodynamic and heat transfer characteristics of the flow are investigated and discussed. The results of these characteristics obtained from non-similar solutions are compared to those obtained from local similarity approach often used by several authors in the last decades. We show that for small shape parameter \(\beta\) and moderate or large values of the slip parameter, the self-similarity of the Falkner-Skan flows is generally lost because of slip boundary conditions. Therefore, the use of the local similarity approach may produce substantial errors for hydrodynamic and thermal characteristics of the flow as compared to non-similar solution. But in contrast, when \(\beta\) becomes larger than 2/3 up to 1, the flow regains its self-similarity character, in this case, the local similarity approach remains valid and may be used. While for \(\beta > 1\) up to 2, the solutions of the boundary layer equations again become non-similar. Furthermore, a special attention was made to evaluate the separation point under rarefaction, the results show that the effect of slip parameter leads to decrease the separation point \(\beta_{\mathrm{s}}\) and it is concluded that separation of the boundary layer should be delayed in the slip flow regime.Methods of controlling flows under the strong hypersonic interaction conditionshttps://www.zbmath.org/1475.760802022-01-14T13:23:02.489162Z"Lipatov, I. I."https://www.zbmath.org/authors/?q=ai:lipatov.igor-ivanovich"Fam, V. K."https://www.zbmath.org/authors/?q=ai:fam.v-kSummary: The methods of the flow control in a laminar boundary layer at local surface cooling are studied. The dependence of the velocity of disturbance propagation upstream on the temperature factor of the body surface is obtained. The methods of controlling the boundary layer flow under the strong viscous-inviscid interaction conditions by means of suppressing the upstream disturbance propagation are investigated.Waves in the gas centrifuge: asymptotic theory and similarities with the atmospherehttps://www.zbmath.org/1475.760812022-01-14T13:23:02.489162Z"Rodal, Marie"https://www.zbmath.org/authors/?q=ai:rodal.marie"Schlutow, Mark"https://www.zbmath.org/authors/?q=ai:schlutow.markSummary: We study the stratified gas in a rapidly rotating centrifuge as a model for the Earth's atmosphere. Based on methods of perturbation theory, it is shown that in certain regimes, internal waves in the gas centrifuge have the same dispersion relation to leading order as their atmospheric siblings. Assuming an air filled centrifuge with a radius of around 50\,cm, the optimal rotational frequency for realistic atmosphere-like waves is around 10 000 revolutions per minute. Using gases of lower heat capacities at constant pressure, such as xenon, the rotational frequencies can be even halved to obtain the same results. Similar to the atmosphere, it is feasible in the gas centrifuge to generate a clear scale separation of wave frequencies and therefore phase speeds between acoustic waves and internal waves. In addition to the centrifugal force, the Coriolis force acts in the same plane. However, its influence on axially homogeneous internal waves appears only as a higher-order correction. We conclude that the gas centrifuge provides an unprecedented opportunity to investigate atmospheric internal waves experimentally with a compressible working fluid.Nonisothermal rarefied gas flow through a long cylindrical channel under arbitrary pressure and temperature dropshttps://www.zbmath.org/1475.760822022-01-14T13:23:02.489162Z"Germider, O. V."https://www.zbmath.org/authors/?q=ai:germider.oksana-vladimirovna"Popov, V. N."https://www.zbmath.org/authors/?q=ai:popov.vasily-nikolaevichSummary: The problem of rarefied gas flow through a long cylindrical channel as a function of the pressure and the temperature maintained at the channel ends is considered on the basis of the \(S\)-model of the Boltzmann kinetic equation. The pressure and temperature drops between the channel ends vary from small values at which the linear transport theory is valid to large values at which the gas molecule mean free path ceases to be constant along the channel. The solution to the model kinetic equation is found by means of the collocation method using the Chebyshev polynomials and rational functions. The mass flow and the pressure in the channel are obtained. Isobaric and isothermal flows are investigated.Force balance in rapidly rotating Rayleigh-Bénard convectionhttps://www.zbmath.org/1475.760832022-01-14T13:23:02.489162Z"Aguirre Guzmán, Andrés J."https://www.zbmath.org/authors/?q=ai:aguirre-guzman.andres-j"Madonia, Matteo"https://www.zbmath.org/authors/?q=ai:madonia.matteo"Cheng, Jonathan S."https://www.zbmath.org/authors/?q=ai:cheng.jonathan-s"Ostilla-Mónico, Rodolfo"https://www.zbmath.org/authors/?q=ai:ostilla-monico.rodolfo"Clercx, Herman J. H."https://www.zbmath.org/authors/?q=ai:clercx.herman-j-h"Kunnen, Rudie P. J."https://www.zbmath.org/authors/?q=ai:kunnen.rudie-p-jSummary: The force balance of rotating Rayleigh-Bénard convection regimes is investigated using direct numerical simulation on a laterally periodic domain, vertically bounded by no-slip walls. We provide a comprehensive view of the interplay between governing forces both in the bulk and near the walls. We observe, as in other prior studies, regimes of cells, convective Taylor columns, plumes, large-scale vortices (LSVs) and rotation-affected convection. Regimes of rapidly rotating convection are dominated by geostrophy, the balance between Coriolis and pressure-gradient forces. The higher-order interplay between inertial, viscous and buoyancy forces defines a subdominant balance that distinguishes the geostrophic states. It consists of viscous and buoyancy forces for cells and columns, inertial, viscous and buoyancy forces for plumes, and inertial forces for LSVs. In rotation-affected convection, inertial and pressure-gradient forces constitute the dominant balance; Coriolis, viscous and buoyancy forces form the subdominant balance. Near the walls, in geostrophic regimes, force magnitudes are larger than in the bulk; buoyancy contributes little to the subdominant balance of cells, columns and plumes. Increased force magnitudes denote increased ageostrophy near the walls. Nonetheless, the flow is geostrophic as the bulk. Inertia becomes increasingly more important compared with the bulk, and enters the subdominant balance of columns. As the bulk, the near-wall flow loses rotational constraint in rotation-affected convection. Consequently, kinetic boundary layers deviate from the expected behaviour from linear Ekman boundary layer theory. Our findings elucidate the dynamical balances of rotating thermal convection under realistic top/bottom boundary conditions, relevant to laboratory settings and large-scale natural flows.Exact solutions for steady convective layered flows with a spatial accelerationhttps://www.zbmath.org/1475.760842022-01-14T13:23:02.489162Z"Burmasheva, N. V."https://www.zbmath.org/authors/?q=ai:burmasheva.natalya-vladimirovna"Prosviryakov, E. Yu."https://www.zbmath.org/authors/?q=ai:prosviryakov.evgenii-yurevichSummary: In this paper, we study non-one-dimensional convective layered flows of a viscous incompressible fluid with a spatial acceleration. We perform the simulation on the base of thermal convection equations in the Boussinesq approximation. We seek for solutions to these equations in a generalized class of exact solutions, where all components of the velocity vector, the pressure, and the temperature represent complete linear forms of two Cartesian coordinates with nonlinear (with respect to to the third Cartesian coordinate) coefficients. We prove that the system of correlations that describe layered flows can be reduced to an overdetermined system of ordinary differential equations. We state and prove two theorems that justify the existence (under a special algebraic condition) and uniqueness of the solution to the resulting overdetermined system.Numerical study for the unsteady space fractional magnetohydrodynamic free convective flow and heat transfer with Hall effectshttps://www.zbmath.org/1475.760852022-01-14T13:23:02.489162Z"Chi, Xiaoqing"https://www.zbmath.org/authors/?q=ai:chi.xiaoqing"Zhang, Hui"https://www.zbmath.org/authors/?q=ai:zhang.hui|zhang.hui.4|zhang.hui.6|zhang.hui.2|zhang.hui.10|zhang.hui.3|zhang.hui.5|zhang.hui.7|zhang.hui.9|zhang.hui.8|zhang.hui.1|zhang.hui.11Summary: In this paper, a numerical research for the problem of unsteady space fractional magnetohydrodynamic (MHD) free convective flow and heat transfer with Hall effects is investigated. We firstly establish a space fractional MHD flow and heat transfer model, which is coupled by the incompressible space fractional Navier-Stokes equations and the heat conduction equation. Then we develop a finite difference spectral decomposition method based on the pressure correction algorithm to solve this nonlinear coupled model. The validity of the proposed numerical scheme is verified and some flow field, temperature field are obtained. We also detailedly analyze the effects of relevant parameters on the space fractional MHD flow and heat transfer.Hall current and radiation effects on unsteady natural convection MHD flow with inclined magnetic fieldhttps://www.zbmath.org/1475.760862022-01-14T13:23:02.489162Z"Rajput, U. S."https://www.zbmath.org/authors/?q=ai:rajput.uday-singh"Gupta, Naval Kishore"https://www.zbmath.org/authors/?q=ai:gupta.naval-kishoreSummary: In the present paper, Hall current and radiation effects on unsteady natural convection MHD flow with inclined magnetic field is studied. The viscous, incompressible and an electrically conducting fluid is considered. This model contains equations of motion, equation of energy and diffusion equation. The system of partial differential equations is transformed to dimensionless equations by using dimensionless variables. Exact solution of governing equations is obtained by Laplace Transform Technique. For analysing the solution of the model, desirable sets of the values of the parameters have been considered. The obtained results of velocity, concentration and temperature have been analysed with the help of graphs drawn for different parameters. The numerical values of Nusselt number have been tabulated. The results of the study may find applications in the field related to the solar physics dealing with the solar cycle, Magnetohydrodynamics sensors, rotating MHD induction machine energy generator, the sunspot development, the structure of rotating magnetic stars etc.Investigation of species-mass diffusion in binary-species boundary layers at high pressure using direct numerical simulationshttps://www.zbmath.org/1475.760872022-01-14T13:23:02.489162Z"Toki, Takahiko"https://www.zbmath.org/authors/?q=ai:toki.takahiko"Bellan, Josette"https://www.zbmath.org/authors/?q=ai:bellan.josetteSummary: Direct numerical simulations of single-species and binary-species temporal boundary layers at high pressure are performed with special attention to species-mass diffusion. The working fluids are nitrogen or a mixture of nitrogen and methane. Mean profiles and turbulent fluctuations of mass fraction show that their qualitative characteristics are different from those of streamwise velocity and temperature, due to the different boundary conditions. In a wall-parallel plane near the wall, the streamwise velocity and temperature have streaky patterns and the fields are similar. However, the mass fraction field at the same location is different from the streamwise velocity and temperature fields indicating that species-mass diffusion is not similar to the momentum and thermal diffusion. In contrast, at the centre and near the edge of the boundary layer, the mass fraction and temperature fields have almost the same pattern, indicating that the similarity between thermal and species-mass diffusion holds away from the wall. The lack of similarity near the wall is traced to the Soret effect that induces a temperature-gradient-dependent species-mass flux. As a result, a new phenomenon has been identified for a non-isothermal binary-species system -- uphill diffusion, which in its classical isothermal definition can only occur for three or more species. A quadrant analysis for the turbulent mass flux reveals that near the wall the Soret effect enhances the negative contributions of the quadrants. Due to the enhancement of the negative contributions, small species-concentration fluid tends to be trapped near the wall.A general analytical approach to study solute dispersion in non-Newtonian fluid flowhttps://www.zbmath.org/1475.760882022-01-14T13:23:02.489162Z"Rana, Jyotirmoy"https://www.zbmath.org/authors/?q=ai:rana.jyotirmoy"Liao, Shijun"https://www.zbmath.org/authors/?q=ai:liao.shijunSummary: The homotopy analysis method (HAM), a general analytic technique for non-linear problems, is applied to analyze the solute dispersion process in non-Newtonian Carreau-Yasuda and Carreau fluids flow in a straight tube with the effect of wall absorption/reaction. Unlike the other analytical methods such as perturbation method, the HAM provides a simple way to get the convergent series solution. Any assumptions of small or high physical quantities are not required for the HAM. It provides us a great freedom to choose the so-called convergence control parameter which is used to guarantee the convergence of series solution. The convergent series solution is obtained by choosing the optimal value of convergence control parameter for which the series converges fastest. The optimal value of convergence control parameter is obtained by minimizing the square residual which also provides the convergence region for the series solution. The previous analytical studies on solute dispersion fail to justify the convergence of the series solution, whereas in this investigation, our results are convergent and valid for all physical parameters. In addition, present results are validated by the numerical and some existing results. This study explains elaborately about the advantage of the homotopy analysis method over perturbation and eigenfunction expansion methods for nonlinear problems. Owing to the great potential and flexibility of the homotopy analysis method, it is a more suitable analytical approach to solve the different types of non-linear problems in science and engineering. Besides, this study helps to gain some knowledge on the transportation process of drugs in the blood flow.Size effect of oscillating columns on mixing: a CFD studyhttps://www.zbmath.org/1475.760892022-01-14T13:23:02.489162Z"Sengia, John"https://www.zbmath.org/authors/?q=ai:sengia.john"James, Alexis"https://www.zbmath.org/authors/?q=ai:james.alexis"Singh, Ramesh"https://www.zbmath.org/authors/?q=ai:singh.ramesh-kumar"Bale, Shivkumar"https://www.zbmath.org/authors/?q=ai:bale.shivkumarSummary: Computational fluid dynamics (CFD) simulations were performed to study the effect of the size of the column on mixing in an oscillating column. Volume of fluid (VOF) method was employed to track the interface, and tracer simulations were carried out to estimate the mixing time. The fluid was assumed to be water, and the ratio of the height of the water in the column and the diameter of the column was equal to 1. The amplitude of the applied oscillation was kept constant at 0.25\,cm, and the frequency was varied from 1 to 20\,Hz. Two cylindrical columns were considered in this work: one with a radius twice the benchmark geometry and the other with a radius half of it. The benchmark geometry was the cylindrical column with radius \(= 0.05\,m\), which was utilized in our previous work [the last author et al., ``Spatially resolved mass transfer coefficient for moderate Reynolds number flows in packed beds: wall effects'', Int. J. Heat Mass Transf. 110, 406--415 (2017; \url{doi:10.1016/j.ijheatmasstransfer.2017.03.052})]. It was observed that the mixing within an oscillating column was nonlinear with respect to the applied oscillation. The mixing time per unit volume was much smaller for the larger column, with similar power per unit mass applied to both the columns. The optimal condition to operate the two columns under consideration were reported. The numerical simulation results were corroborated by the stability chart determined theoretically by solving a series of Mathieu equation, contour plots through the column, and the snapshots of the free surface.Lower-dimensional nonlinear Brinkman's law for non-Newtonian flows in a thin porous mediumhttps://www.zbmath.org/1475.760902022-01-14T13:23:02.489162Z"Anguiano, María"https://www.zbmath.org/authors/?q=ai:anguiano.maria"Suárez-Grau, Francisco J."https://www.zbmath.org/authors/?q=ai:suarez-grau.francisco-javierRelying on a combination of ideas involving dimension reduction techniques, monotonicity arguments, as well as an adaptation of the periodic unfolding method, the authors study a power-law Stokes model posed in a thin porous medium (with suitably scaled very thin microstructures). In the homogenization limit, they derive a lower-dimensional Brinkmann model for flow through such porous media.
Reviewer: Adrian Muntean (Karlstad)A mixed dimensional model for the interaction of a well with a poroelastic materialhttps://www.zbmath.org/1475.760912022-01-14T13:23:02.489162Z"Cerroni, Daniele"https://www.zbmath.org/authors/?q=ai:cerroni.daniele"Radu, Florin"https://www.zbmath.org/authors/?q=ai:radu.florin-adrian"Zunino, Paolo"https://www.zbmath.org/authors/?q=ai:zunino.paoloSummary: We develop a mathematical model for the interaction of the mechanics of a three-dimensional permeable reservoir or aquifer with the flow through wells. We apply a model reduction technique that represents the wells as one-dimensional channels with arbitrary configuration in the space and we introduce proper coupling conditions to account for the interaction of the wells with the bulk region. The resulting problem consists of coupled partial differential equations defined on manifolds with heterogeneous dimensionality. To highlight the potential of this modeling approach in the description of realistic scenarios, we combine it with a suitable discretization method and we discuss the results of preliminary simulations on an idealized test case containing two wells.
For the entire collection see [Zbl 1471.65009].Hydraulic fracture induced by water injection in weak rockhttps://www.zbmath.org/1475.760922022-01-14T13:23:02.489162Z"Gao, Yue"https://www.zbmath.org/authors/?q=ai:gao.yue"Detournay, Emmanuel"https://www.zbmath.org/authors/?q=ai:detournay.emmanuelSummary: A two-dimensional model of a hydraulic fracture propagating in a weakly consolidated, highly permeable reservoir rock during a waterflooding operation is described in this paper. The model recognizes the essential differences that exist between this class of fractures and conventional hydraulic fracturing treatments of oil and gas wells, namely: (i) the large-scale perturbations of pore pressure and the associated poroelastic effects caused by extended injection time; (ii) the extremely small volume of fluid stored in the fracture compared with the injected volume; and (iii) the leakage of water from both the borehole and the propagating fracture. The model consists of a set of equations encompassing linear elastic fracture mechanics, porous media flow and lubrication theory. Three asymptotic solutions applicable at different time regimes are found theoretically, and numerical results are obtained from the discretized governing equations. The solution reveals that the injection pressure does not evolve monotonically, as it increases with time in the early time radial-flow regime but decreases in the late time fracture-flow regime. Thus, the peak injection pressure does not correspond to a breakdown of the formation, as usually assumed, but rather to a transition between two regimes of porous media flow. However, this problem exhibits an extreme sensitivity of the time scales on a dimensionless injection rate \(\mathcal{I} \). If \(\mathcal{I} \lessapprox 1\), the time to reach the peak pressure could become so large that it cannot be observed in field operations, i.e. the fracture remains hydraulically invisible. Finally, it is found that poroelasticity significantly affects the response of the system, by increasing the injection pressure and delaying the time at which the peak pressure takes place.An efficient numerical scheme for fully coupled flow and reactive transport in variably saturated porous media including dynamic capillary effectshttps://www.zbmath.org/1475.760932022-01-14T13:23:02.489162Z"Illiano, Davide"https://www.zbmath.org/authors/?q=ai:illiano.davide"Pop, Iuliu Sorin"https://www.zbmath.org/authors/?q=ai:pop.iuliu-sorin"Radu, Florin Adrian"https://www.zbmath.org/authors/?q=ai:radu.florin-adrianSummary: In this paper we study a model for the transport of an external component, e.g., a surfactant, in variably saturated porous media. We discretize the model in time and space by combining a backward Euler method with the linear Galerkin finite elements. The Newton method and the L-Scheme are employed for the linearization and the performance of these schemes is studied numerically. A special focus is set on the effects of dynamic capillarity on the transport equation.
For the entire collection see [Zbl 1471.65009].Mathematical model and method for solving the problem of non-isothermal gas and liquid filtration flow during dissociation of gas hydrateshttps://www.zbmath.org/1475.760942022-01-14T13:23:02.489162Z"Musakaev, N. G."https://www.zbmath.org/authors/?q=ai:musakaev.nasil-gabsalyamovich"Belskikh, D. S."https://www.zbmath.org/authors/?q=ai:belskikh.denis-sergeevich"Borodin, S. L."https://www.zbmath.org/authors/?q=ai:borodin.stansilav-leonidovichSummary: The development of a mathematical model of the filtration flow during dissociation of gas hydrates for the two-dimensional case is researched considering the motion of both components of the gas hydrate (water and gas). Non-isothermal effects and the gas being not ideal while filtering liquid and gas are considered; the hydrate dissociation process is assumed to be in equilibrium. A method is developed for solving the system of equations of the mathematical model using an implicit difference scheme, tridiagonal matrix algorithm and simple iterations, as well as a developed method for calculating hydrate saturation. This method allows to find the spatial distributions of the main parameters of the gas-liquid filtration flow (temperature, pressure and phases saturations) for each moment in time, as well as position of the boundary of phase transitions.Mathematical modeling of the gas hydrate formation process in a zonal heterogeneous porous reservoirhttps://www.zbmath.org/1475.760952022-01-14T13:23:02.489162Z"Musakaev, N. G."https://www.zbmath.org/authors/?q=ai:musakaev.nnail-gabsalyamovich|musakaev.nasil-gabsalyamovich|musakaev.nail-gabsalyamovich"Borodin, S. L."https://www.zbmath.org/authors/?q=ai:borodin.stansilav-leonidovich|borodin.stanislav-leonidovichSummary: Mathematical modeling of the gas hydrate formation in a zonal heterogeneous porous reservoir, consisting of high- and low-permeability zones, has been carried out. This process was studied for the case of gas injection into a reservoir, the pores of which in the initial state are filled with gas and water. The results of numerical experiments are presented and analyzed when the injection well is located in a high- or low-permeable zone.Entropy generation on electromagnetohydrodynamic flow through a porous asymmetric micro-channelhttps://www.zbmath.org/1475.760962022-01-14T13:23:02.489162Z"Ranjit, N. K."https://www.zbmath.org/authors/?q=ai:ranjit.n-k"Shit, G. C."https://www.zbmath.org/authors/?q=ai:shit.g-cSummary: We analyze the heat transfer phenomena in a narrow confinement filled with couple stress fluid (taking into account molecule size effect) driven by the simultaneous influence of pressure gradient, electrical potential and the peristaltic pumping in the presence of magnetic field. The effects of Joule heating, permeability of the porous medium and dissipation of energy are taken into account. Entropy generation in terms of Bejan profile and the Nusselt number under different parameters are investigated. The analytical method has been invoked to find the closed from solution of the thermo-fluidic governing equations. The study reveals that the zeta potential has significant importance in controlling velocity and thermal response in the system. The Joule heating effect and Brinkman number both are equally responsible for enhancement of thermal irreversibility measured in terms of Bejan number profile. Thus, the study bears potential applications in industrial and biomedical technology for developing microfluidic devices.Global random walk solutions for flow and transport in porous mediahttps://www.zbmath.org/1475.760972022-01-14T13:23:02.489162Z"Suciu, Nicolae"https://www.zbmath.org/authors/?q=ai:suciu.nicolae-petruSummary: This article presents a new approach to solve the equations of flow in heterogeneous porous media by using random walks on regular lattices. The hydraulic head is represented by computational particles which are spread globally from the lattice sites according to random walk rules, with jump probabilities determined by the hydraulic conductivity. The latter is modeled as a realization of a random function generated as a superposition of periodic random modes. One- and two-dimensional numerical solutions are validated by comparisons with analytical manufactured solutions. Further, an ensemble of divergence-free velocity fields computed with the new approach is used to conduct Monte Carlo simulations of diffusion in random fields. The transport equation is solved by a global random walk algorithm which moves computational particles representing the concentration of the solute on the same lattice as that used to solve the flow equations. The integrated flow and transport solution is validated by a good agreement between the statistical estimations of the first two spatial moments of the solute plume and the predictions of the stochastic theory of transport in groundwater.
For the entire collection see [Zbl 1471.65009].Solution of a two-dimensional problem of the theory of stationary liquid filtration through an earth dam with the broken backslopehttps://www.zbmath.org/1475.760982022-01-14T13:23:02.489162Z"Tsitskishvili, Z. A."https://www.zbmath.org/authors/?q=ai:tsitskishvili.z-a"Tsitskishvili, A. R."https://www.zbmath.org/authors/?q=ai:tsitskishvili.avtandil-r"Tsitskishvili, R. A."https://www.zbmath.org/authors/?q=ai:tsitskishvili.r-aSummary: The paper proposes a theoretical solution scheme for a two-dimensional problem of the theory of stationary liquid filtration through an earth dam. The dam foundation is water-proof. The dam backslope is the broken line consisting of two segments of the straight line which forms with the dam foundation an angle \(\pi/2\), whereas the tail-water level is equal to zero.Self-similar fault slip in response to fluid injectionhttps://www.zbmath.org/1475.760992022-01-14T13:23:02.489162Z"Viesca, Robert C."https://www.zbmath.org/authors/?q=ai:viesca.robert-cSummary: There is scientific and industrial interest in understanding how geologic faults respond to transient sources of fluid. Natural and artificial sources can elevate pore fluid pressure on the fault frictional interface, which may induce slip. We consider a simple boundary value problem to provide an elementary model of the physical process and to provide a benchmark for numerical solution procedures. We examine the slip of a fault that is an interface of two elastic half-spaces. Injection is modelled as a line source at constant pressure and fluid pressure is assumed to diffuse along the interface. The resulting problem is an integro-differential equation governing fault slip, which has a single dimensionless parameter. The expansion of slip is self-similar and the rupture front propagates at a factor \(\lambda\) of the diffusive length scale \(\sqrt{\alpha t}\). We identify two asymptotic regimes corresponding to \(\lambda\) being small or large and perform a perturbation expansion in each limit. For large \(\lambda\), in the regime of a so-called critically stressed fault, a boundary layer emerges on the diffusive length scale, which lags far behind the rupture front. We demonstrate higher-order matched asymptotics for the integro-differential equation, and in doing so, we derive a multipole expansion to capture successive orders of influence on the outer problem for fault slip for a driving force that is small relative to the crack dimensions. Asymptotic expansions are compared with accurate numerical solutions to the full problem, which are tabulated to high precision.A study of transient flows with interfaces using numerical solution of Navier-Stokes equationshttps://www.zbmath.org/1475.761002022-01-14T13:23:02.489162Z"Aleksyuk, A. I."https://www.zbmath.org/authors/?q=ai:aleksyuk.andrey-i"Shkadov, V. Ya."https://www.zbmath.org/authors/?q=ai:shkadov.victor-yaSummary: Flows of two immisible fluids are considered taking into account the capillary and gravity forces. The flow is described using a viscous incompressible fluid model within a two-dimensional formulation. The Navier-Stokes equations are solved numerically by an extended finite-element method, which allows for the presence of a strong discontinuity on the interface. The interface location is tracked using the level set method. This approach makes it possible to study flows with a varying topology of the interface. The calculation results are presented for the problems of a rising 2D bubble, development of the Rayleigh-Taylor instability, and a film flowing down a vertical wall in an extended region.Expansion waves accompanying material evaporation into a vacuum or a low-density mediumhttps://www.zbmath.org/1475.761012022-01-14T13:23:02.489162Z"Kusov, A. L."https://www.zbmath.org/authors/?q=ai:kusov.a-l"Lunev, V. V."https://www.zbmath.org/authors/?q=ai:lunev.v-vSummary: The problem of one-dimensional intense evaporation waves is considered. It concerns with unsteady instantaneous expansion of overheated material vapors into a vacuum or a low-density medium from a plate, a cylinder, or a sphere, whereupon constant (``sonic'') boundary conditions are imposed on the surfaces of these bodies.Modeling of the dynamics of a gas bubble in liquid near a curved wallhttps://www.zbmath.org/1475.761022022-01-14T13:23:02.489162Z"Malakhov, V. G."https://www.zbmath.org/authors/?q=ai:malakhov.v-gSummary: The efficiency of modeling of the axisymmetric dynamics of a gas bubble near a curved rigid wall by the boundary element method using the fundamental solution of the Laplace equation for an unbounded domain is numerically studied. For this purpose, the problems of the collapse of a bubble near a flat wall and the expansion and subsequent collapse of a bubble near the concave and convex walls are considered. To assess the effectiveness, the results of calculations of these problems are compared with the known results of their calculations using their fundamental solutions for the areas bounded by those walls. The results show the dependence of the numerical solution on the radius of the computational domain on the wall, the number of cells when the domain is uniformly partitioned, and the number of cells when it is non-uniformly partitioned with condensation toward the axis of symmetry along a geometric progression.Evaporation of multiple dropletshttps://www.zbmath.org/1475.761032022-01-14T13:23:02.489162Z"Masoud, Hassan"https://www.zbmath.org/authors/?q=ai:masoud.hassan"Howell, Peter D."https://www.zbmath.org/authors/?q=ai:howell.peter-d"Stone, Howard A."https://www.zbmath.org/authors/?q=ai:stone.howard-aSummary: We derive an accurate estimate for the diffusive evaporation rates of multiple droplets of different sizes and arbitrary contact angles placed on a horizontal substrate. The derivation, which is based on a combination of Green's second identity and the method of reflections, simply makes use of the solution for the evaporation of a single droplet. The theoretical results can serve as a guide for future computational and experimental studies on the collective evaporation of arrays of droplets, as well as similar multi-body, diffusion-dominated transport problems.Scale-dependent anisotropy, energy transfer and intermittency in bubble-laden turbulent flowshttps://www.zbmath.org/1475.761042022-01-14T13:23:02.489162Z"Ma, Tian"https://www.zbmath.org/authors/?q=ai:ma.tian"Ott, Bernhard"https://www.zbmath.org/authors/?q=ai:ott.bernhard"Fröhlich, Jochen"https://www.zbmath.org/authors/?q=ai:frohlich.jochen"Bragg, Andrew D."https://www.zbmath.org/authors/?q=ai:bragg.andrew-dSummary: Data from direct numerical simulations of disperse bubbly flows in a vertical channel are used to study the effect of the bubbles on the carrier-phase turbulence. We developed a new method, based on an extension of the barycentric map approach, that allows us to quantify and visualize the anisotropy and componentiality of the flow at any scale. Using this we found that the bubbles significantly enhance anisotropy in the flow at all scales compared with the unladen case, and that for some bubble cases, very strong anisotropy persists down to the smallest scales of the flow. The strongest anisotropy observed was for the cases involving small bubbles. Concerning the energy transfer among the scales of the flow, our results indicate that for the bubble-laden cases, the energy transfer is from large to small scales, just as for the unladen case. However, there is evidence of an upscale transfer when considering the transfer of energy associated with particular components of the velocity field. Although the direction of the energy transfer is the same with and without the bubbles, the behaviour of the energy transfer is significantly modified by the bubbles, suggesting that the bubbles play a strong role in altering the activity of the nonlinear term in the flow. The skewness of the velocity increments also reveals a strong effect of the bubbles on the flow, changing both its sign and magnitude compared with the single-phase case. We also consider the normalized forms of the fourth-order structure functions, and the results reveal that the introduction of bubbles into the flow strongly enhances intermittency in the dissipation range, but suppresses it at larger scales. This strong enhancement of the dissipation-scale intermittency has significant implications for understanding how the bubbles might modify the mixing properties of turbulent flows.Numerical simulation of Couette-Taylor-Poiseuille two-phase flowhttps://www.zbmath.org/1475.761052022-01-14T13:23:02.489162Z"Morenko, I. V."https://www.zbmath.org/authors/?q=ai:morenko.i-vSummary: A numerical study of the Couette-Taylor-Poiseuille two-phase flow is presented in this work. The proposed mathematical model takes into account the nonstationarity and three-dimensionality of the process of medium motion and rotation of the surface of the inner cylinder, as well as surface tension and the action of gravity. The developed numerical technique was tested on the solution of the problem of Couette-Taylor single-phase flow, which is the limiting case of a two-phase flow, when the volume concentration of the gas phase is zero. Two regimes of a two-phase flow are obtained. At low Reynolds numbers, a stratified flow regime is observed. In the second regime of two-phase flow, the gas phase is localized along a helical line along the surface of the inner cylinder. It is shown that the dimensionless torque increases when the gas phase is added to the flow.Influence of liquid pressure on the collapse of a vapor bubble in cold and cool acetonehttps://www.zbmath.org/1475.761062022-01-14T13:23:02.489162Z"Toporkov, D. Yu."https://www.zbmath.org/authors/?q=ai:toporkov.d-yuSummary: The features of the fluid compression in a vapor bubble during its collapse in cold (273 K) and cool (293 K) acetone are studied. The liquid pressure \(p_0\) is varied in the range 0.12--5 bar. The full hydrodynamic model is used in vapor and liquid. The non-stationary heat conductivity of both fluids and non-equilibrium mass transfer across the bubble surface are taken into account. Realistic wide-range equations of state are applied. It is shown that as the liquid pressure \(p_0\) is diminished, the depth of the bubble collapse decreases in cold acetone, but grows in cool acetone. The maximum of the collapse rate decreases monotonically in cool acetone. In cold acetone it is reduced only in an interval bounded by a certain value of \(p_0\), and then it increases. As a result, with decreasing \(p_0\) of cool acetone, the vapor in the bubble is compressed first by radially convergent shock waves, then by isentropic waves, and after that its nearly uniform compression takes place, whereas only the first scenario is realized in cold acetone.Numerical study of bubble rising motion in a vertical wedge-shaped channel based on a modified level set methodhttps://www.zbmath.org/1475.761072022-01-14T13:23:02.489162Z"Zhang, Yifu"https://www.zbmath.org/authors/?q=ai:zhang.yifu"Liang, Bing"https://www.zbmath.org/authors/?q=ai:liang.bing"Ni, Jingfeng"https://www.zbmath.org/authors/?q=ai:ni.jingfengSummary: A modified level set method coupled with local-reinitialized process and volume-corrected method is employed to simulate bubble motions in complex channels. The volume-corrected process helps to adjust the mass loss due to bubble simulation by standard level set method and local reinitialization of level set function eliminates the numerical dissipation due to nonorthogonality of the boundary mesh. For solving the problem of two-phase flow with a complex boundary, the mesh generation is employed in the physical plane in body-fitted coordinates. All parameters in the physical domain are transformed into a computational domain, where the governing equations are discretized on collocated grids using the finite volume method and the SIMPLE algorithm to decouple the velocities and the pressure. The continuum surface force model is employed to deal with the surface tension of bubbles. By simulating bubble rising in a wedge-shaped channel, the method is demonstrated to be effective to solve the bubble motion in a complex physical plane.Kinetic theory of discontinuous rheological phase transition for a dilute inertial suspensionhttps://www.zbmath.org/1475.761082022-01-14T13:23:02.489162Z"Hayakawa, Hisao"https://www.zbmath.org/authors/?q=ai:hayakawa.hisao"Takada, Satoshi"https://www.zbmath.org/authors/?q=ai:takada.satoshi.1Summary: A kinetic theory for a dilute inertial suspension under a simple shear is developed. With the aid of the corresponding Boltzmann equation, it is found that the flow curves (the relations between the stress and the strain rate) exhibit the crossovers from the Newtonian to the Bagnoldian for a granular suspension and from the Newtonian to a fluid having a viscosity proportional to the square of the shear rate for a suspension consisting of elastic particles, respectively. The existence of the negative slope in the flow curve directly leads to a discontinuous shear thickening (DST). This DST corresponds to the discontinuous transition of the kinetic temperature between a quenched state and an ignited state. The results of the event-driven Langevin simulation of hard spheres perfectly agree with the theoretical results without any fitting parameter. The introduction of an attractive interaction between particles is also another source of the DST in dilute suspensions. Namely, there are two discontinuous jumps in the flow curve if the suspension particles have the attractive interaction.Solution three-phase fluid flow problem under thermal influence on the reservoirhttps://www.zbmath.org/1475.761092022-01-14T13:23:02.489162Z"Tsepaev, A. V."https://www.zbmath.org/authors/?q=ai:tsepaev.a-vSummary: The work is devoted to the methods of solving three-phase nonisothermal fluid flow problems in the reservoirs. The model of steam assisted gravity drainage is considered. The temperature of the fluid and of the porous medium are considered to be the same. To determine the temperature is used the law of energy conservation. The methods for solving three-phase nonisothermal flow problems in porous medium based on the decomposition methods are proposed. The proposed methods are implemented on the heterogeneous computing systems.Counter-rotating flow in coaxial cylinders under an axial magnetic fieldhttps://www.zbmath.org/1475.761102022-01-14T13:23:02.489162Z"Mahfoud, B."https://www.zbmath.org/authors/?q=ai:mahfoud.brahim"Laouari, A."https://www.zbmath.org/authors/?q=ai:laouari.a"Hadjadj, A."https://www.zbmath.org/authors/?q=ai:hadjadj.abdellah"Benhacine, H."https://www.zbmath.org/authors/?q=ai:benhacine.hSummary: Numerical simulations are presented of swirling flow in vertical annuli filled with a liquid metal with counter-rotating end disks under an axial magnetic field. Two coaxial cylinders where a liquid metal was placed in the annular gap having an aspect ratio (height/radius) \(\gamma = 2\) are considered. The bottom and top disks are assumed to rotate at the opposite (counter-rotating) angular velocities. Six annular gaps \(R = 0.9\), 0.8, 0.7, 0.6, 0.5 and 0.4 were studied. The governing Navier-Stokes and potential equations are solved by using the finite-volume method. The results show that different complex flow appears as the annular gap become larger. Asymmetric \(m = 2\) and 3 azimuthal modes are observed. The presence of the magnetic field results to fluid deceleration and, thus, to flow stabilization. The stability diagram \((\mathrm{Re}_{cr}-\mathrm{R})\) corresponding to the transition from axisymmetric to non-axisymmetric flow for increasing values of the Hartmann number is obtained.Investigation of effective parameters on Gorlov vertical axis wind turbinehttps://www.zbmath.org/1475.761112022-01-14T13:23:02.489162Z"Moghimi, M."https://www.zbmath.org/authors/?q=ai:moghimi.mahdi|moghimi.mohammad-bagher-farshbaf|moghimi.mohsen-h|moghimi.m-f|moghimi.m-a"Motawej, H."https://www.zbmath.org/authors/?q=ai:motawej.hSummary: In this paper, we aim to develop a low-cost model for evaluating the aerodynamic design and performance of Gorlov vertical axis wind turbine (VAWT). To this end, a double multiple stream tube (DMST) model, which is based on the blade element momentum theory (BEM) has been developed for Gorlov VAWTs. The developed model is validated by comparing the obtained results with the available results in the literature; in addition, overall evaluation on the effects of geometrical and operational parameters, including profile of the blade airfoil, number of blades, helical angle, chord length, aspect ratio and free wind velocity have been performed for aerodynamic performance and the torque coefficient curves of Gorlov VAWT. Considering the results of parametrical evaluation on Gorlov turbine, maximum power coefficient \(({{C}_P})\) is 0.479 for the tip speed ratio \((\lambda)\) of 3.5 in NACA 0018 airfoil. In addition, it becomes evident that the number of blades and helical angle are important parameters in reducing the aerodynamic loads and improving the rotor stability. As the blade chord length or aspect ratio increases, the performance improves at low \(\lambda\) values; however, it decrease at high \(\lambda\) values and peak \({{C}_P}\). Moreover, self-starting behavior has been improved with increasing the blade chord length or free wind velocity and deteriorated by the usage of thinner airfoils. For the studied Gorlov turbine, the performance curves become wider until free wind velocity reaches to the rated velocity, which is 12 m/s for the studied Gorlov turbine.Significance of Coriolis force on Eyring-Powell flow over a rotating non-uniform surfacehttps://www.zbmath.org/1475.761122022-01-14T13:23:02.489162Z"Oke, Abayomi Samuel"https://www.zbmath.org/authors/?q=ai:oke.abayomi-samuel"Mutuku, Winifred Nduku"https://www.zbmath.org/authors/?q=ai:mutuku.winifred-ndukuSummary: Coriolis force plays significant roles in natural phenomena such as atmospheric dynamics, weather patterns, etc. Meanwhile, to circumvent the unreliability of Newtonian law for flows involving varying speed, Eyring-Powell fluid equations are used in computational fluid dynamics. This paper unravels the significance of Coriolis force on Eyring-Powell fluid over the rotating upper horizontal surface of a paraboloid of revolution. Relevant body forces are included in the Navier-Stokes equations to model the flow of non-Newtonian Eyring-Powell fluid under the influence of Coriolis force. Using similarity transformation, the governing equations are nondimensionalized, thereby transforming the nonlinear partial differential equations to a system of boundary value nonlinear ordinary differential equations. The shooting technique is adopted to convert the boundary value problem to an initial value problem, which is in turn solved using the Runge-Kutta-Gill Scheme. At low Coriolis force, temperature profiles increase as Eyring-Powell parameter increases, whereas at high Coriolis force, temperature profiles decrease with increasing Eyring-Powell parameter.CFD analysis of tip clearance effects on the performance of transonic axial compressorhttps://www.zbmath.org/1475.761132022-01-14T13:23:02.489162Z"Sohail, M. U."https://www.zbmath.org/authors/?q=ai:sohail.muhammad-umer|sohail.muhammad-umair"Hamdani, H. R."https://www.zbmath.org/authors/?q=ai:hamdani.hossein-raza"Pervez, Kh."https://www.zbmath.org/authors/?q=ai:pervez.khSummary: Ongoing development concerning to increase engine thrust to weight ratio in a gas turbine engine which gives rises to extremely loaded compressor stages. Highly loaded compressors stability is associated with low energy tip leakage flow (TLF) which leads to the flow blockage and thermodynamic losses. This causes greater adverse effects in transonic axial flow compressors owing to the interaction of shock wave and tip leakage flow. The current paper aims for a detail investigation of tip clearances flow field region and their profound effects on aerodynamic performance, stability range and stability margin of low aspect modern transonic axial flow compressor through mathematical modeling and numerical simulation using ANSYS CFX software. Detail rotor flow field was numerically and computationally investigated at zero tip clearance, above and below of design tip clearance to conclude the performance of compressor at suitable tip clearance. A mathematical model has been established to predict the behavior of compressor rotor at choking, peak efficiency and near stall point mass flow rate conditions at different tip clearances. Mathematical model is developed to predict the behavior of compressor at different tip clearances. Furthermore, mathematical-based model results are validated with the computational results. The eminence of both model prediction and the numerical solution was assessed, and conclusions were drawn.Comparison of air-breathing engines with slow and detonation combustionhttps://www.zbmath.org/1475.761142022-01-14T13:23:02.489162Z"Egoryan, A. D."https://www.zbmath.org/authors/?q=ai:egoryan.a-d"Kraiko, A. N."https://www.zbmath.org/authors/?q=ai:kraiko.a-nSummary: The ramjets of different schemes with slow and detonation combustion are compared. Steady and unsteady processes in these engines are described by simple models of gasdynamics and thermodynamics, detonation waves, air deceleration in air intakes, and combustion product acceleration in supersonic sections of nozzles. Within the framework of these models, at a fixed adiabatic exponent the characteristics of any engine depend on two parameters, namely, the flight Mach number and the dimensionless combustion heat of the combustible mixture. The comparison performed for all actual values of these parameters, together with an analysis of thermodynamic cycles and one-dimensional time-dependent calculations (for the engines with combustion in traveling detonation waves), confirmed the importance of taking the unsteady processes in combustors into account. The comparison made in this study is actual, due to frequent claims about a possible considerable increase in the thrust characteristics on replacement of ramjets with slow combustion under a constant pressure by engines with combustion in pulsed or rotating detonation waves (pulse-detonation engines (PDE) or rotating detonation engines (RDE)). Usually, these assertions are made on the basis of the comparison of the thermal efficiencies and specific thrusts and impulses calculated according to these values. In the case of unsteady flow in the combustor, the recalculation of the thrusts and impulses according to the thermal efficiency overestimates their values. The validity of this statement for multichambered PDEs is confirmed by time-dependent calculations. In the case of instantaneous opening and closing of the entrance into the detonation chambers and an instantaneous, without energy expenditures, detonation wave initiation, the PDE thrust is less than the ramjet thrust, starting from small supersonic flight Mach numbers. Analogous calculations for the RDEs are unjustified due to the passage into a rotating noninertial coordinate system.AC electrohydrodynamic Landau-Squire flows around a conducting nanotiphttps://www.zbmath.org/1475.761152022-01-14T13:23:02.489162Z"Chen, Jyun-An"https://www.zbmath.org/authors/?q=ai:chen.jyun-an"Miloh, Touvia"https://www.zbmath.org/authors/?q=ai:miloh.touvia"Kaveevivitchai, Watchareeya"https://www.zbmath.org/authors/?q=ai:kaveevivitchai.watchareeya"Wei, Hsien-Hung"https://www.zbmath.org/authors/?q=ai:wei.hsienhungSummary: Utilizing the joint singular natures of electric field and hydrodynamic flow around a sharp nanotip, we report new electrohydrodynamic Landau-Squire-type flows under the actions of alternating current (AC) electric fields, markedly different from the classical Landau-Squire flow generated by pump discharge using nanotubes or nanopores. Making use of the locally diverging electric field prevailing near the conical tip, we are able to generate a diversity of AC electrohydrodynamic flows with the signature of a \(1/r\) point-force-like decay at distance \(r\) from the tip. Specifically, we find AC electrothermal jet and Faradaic streaming out of the tip at applied frequencies in the MHz and \(10^2\) Hz regimes, respectively. Yet at intermediate frequencies of 1--100 kHz, the jet flow can be reversed to an AC electro-osmotic impinging flow. The characteristics of these AC jet flows are very distinct from AC flows over planar electrodes. For the AC electrothermal jet, we observe experimentally that its speed varies with the driving voltage \(V\) as \(V^3\), in contrast to the common \(V^4\) dependence according to the classical theory reported by \textit{A. Ramos} et al. [``Ac electrokinetics: a review of forces in microelectrode structures'', J. Phys. D: Appl. Phys. 31, No. 18, 2338--2353 (1998; \url{doi:10.1088/0022-3727/31/18/021})]. Additionally, the flow speed does not increase with the solution conductivity as commonly thought. These experimental findings can be rationalized by means of local Joule heating and double layer charging mechanisms in such a way that the nanotip actually becomes a local hotspot charged with heated tangential currents. The measured speed of the AC Faradaic streaming is found to vary as \(V^{3/2} \log V\), which can be interpreted by the local Faradaic leakage in balance with tangential conduction. These unusual flow characteristics signify that a conical electrode geometry may fundamentally alter the features of AC electrohydrodynamic flows. Such peculiar electrohydrodynamic flows may also provide new avenues for expediting molecular sensing or sample transport in prevalent electrochemical or microfluidic applications.Approximate method of the simultaneous rotation problem of the porous plate and fluid with account of magnetic field and heat transfer in case of variable eleqtroconductivityhttps://www.zbmath.org/1475.761162022-01-14T13:23:02.489162Z"Jikidze, L."https://www.zbmath.org/authors/?q=ai:jikidze.levan|jikidze.l-a"Tsutskiridze, V."https://www.zbmath.org/authors/?q=ai:tsutskiridze.v-n|tsutskiridze.vardenSummary: In this paper by means of consistent approximation has been studied unsteady problem of the simultaneous rotation of the infinite porous plate and fluid with account of magnetic field and heat transfer in case of variable electroconductivity, when into the plate takes place injection of the same flow with \(v_w(t)\) speed. \par To determine the thickness of the dynamic and thermal boundary layers, differential equations are obtained and found the exact solutions in special cases when the injection velocity varies according to different laws and between the thicknesses of a functional dependence of the form \(\delta_T(t)= \gamma\delta(t)\). \par All physical characteristics of the flow are calculated.On the quasi-static approximation in the finite magnetic Reynolds number magnetohydrodynamic flow past a circular cylinderhttps://www.zbmath.org/1475.761172022-01-14T13:23:02.489162Z"Sarkar, Subharthi"https://www.zbmath.org/authors/?q=ai:sarkar.subharthi"Ghosh, Samit"https://www.zbmath.org/authors/?q=ai:ghosh.samit"Sivakumar, R."https://www.zbmath.org/authors/?q=ai:sivakumar.rajagopalan"Sekhar, T. V. S."https://www.zbmath.org/authors/?q=ai:sekhar.t-v-sSummary: We consider the classical problem of magnetohydrodynamic (MHD) flow past a circular cylinder in the presence of an imposed magnetic field aligned to the flow. Our analysis includes the computation of magnetic field in the interior of the cylinder because in an experimental setup, the magnetic field will naturally pass through the cylinder. As such, we have solved the Maxwell's equations both in the fluid flow region as well as in the interior of the cylinder with appropriate continuity conditions for magnetic field as it penetrates the cylinder. The fully nonlinear MHD equations are solved numerically using a highly accurate finite difference scheme. The influence of magnetic field in controlling boundary layer separation is discussed through the analysis of pressure gradient and the radial and transverse velocity gradients. In fact, magnetic field penetrated inside the cylinder helps to suppress flow separation more effectively than otherwise. A non-monotonic behavior of interaction parameter on the flow separation is observed for low values of magnetic Reynolds numbers (\(Rm\)). Most importantly, we examine the realm of Quasi-Static approximation in the two-dimensional MHD flows against the corresponding computationally expensive fully nonlinear MHD solutions. Our results suggest that even if \(Rm = 0 . 5\), the percentage error in using quasi-static approximation can reach up to 17.5\%. Thus, we have analyzed and quantified the differences between the fully nonlinear treatment and the quasi-static approximation for this classical flow configuration for the first time.A remark on the time-decay estimates for the compressible magnetohydrodynamic systemhttps://www.zbmath.org/1475.761182022-01-14T13:23:02.489162Z"Shi, Weixuan"https://www.zbmath.org/authors/?q=ai:shi.weixuan"Zhang, Jianzhong"https://www.zbmath.org/authors/?q=ai:zhang.jianzhong|zhang.jianzhong.1Summary: The present paper is dedicated to the optimal time-decay estimates of global strong solutions near constant equilibrium (away from vacuum) to the compressible magnetohydrodynamic (MHD) equations in the \(L^p\) critical Besov spaces. In which we claim a new low-frequency assumption that plays a key role in the large-time behavior of solutions. Precisely, we exhibit that if the low frequencies of initial data belong to some Besov space \(B_{2,\infty}^{-s_1}\) with \(s_1 \in (I1 - \frac{d}{2}, s_0)(s_0 \triangleq \frac{2d}{p} - \frac{d}{2})\), then the \(L^p\) norm (the slightly stronger \(B_{p,1}^0\) norm in fact) of strong solutions has the optimal decay \(t^{-\frac{s_1}{2}-\frac{d}{2}(\frac{1}{2}-\frac{1}{p})} (t^{-\frac{d}{2p}}\) if \(s_1= s_0)\) for \(t \to \infty\), which improve the results of \textit{W. Shi} and \textit{J. Xu} [J. Hyperbolic Differ. Equ. 15, No. 2, 259--290 (2018; Zbl 1393.76142)]. The proof mainly depends on a \textit{sharp time-weighted energy estimates} in light of low and high frequencies for the solutions. As a by-product, those optimal time-decay rates of \(B_{2,\infty}^{-s_1}\)-\(L^r\) type are also captured in the critical framework.Global small solutions to the inviscid Hall-MHD systemhttps://www.zbmath.org/1475.761192022-01-14T13:23:02.489162Z"Zhai, Xiaoping"https://www.zbmath.org/authors/?q=ai:zhai.xiaoping"Li, Yongsheng"https://www.zbmath.org/authors/?q=ai:li.yongsheng"Zhao, Yajuan"https://www.zbmath.org/authors/?q=ai:zhao.yajuanSummary: The local existence of smooth solutions to the inviscid Hall-MHD system has been obtained since [\textit{D. Chae} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 31, No. 3, 555--565 (2014; Zbl 1297.35064)]. However, as far as we know, how to construct the global small solutions to the inviscid Hall-MHD system is still an open problem. In the present paper, we give a positive answer in \(\mathbb{T}^3\) when the initial magnetic field is close to a background magnetic field satisfying the Diophantine condition.Effect of magnetic and perturbation parameters on blood flow distribution through an arteryhttps://www.zbmath.org/1475.761202022-01-14T13:23:02.489162Z"Ahmad, Sultan"https://www.zbmath.org/authors/?q=ai:ahmad.sultan"Al-Johani, A. F."https://www.zbmath.org/authors/?q=ai:aljohani.abdulrahman-f"Sahu, Subrata Kumar"https://www.zbmath.org/authors/?q=ai:sahu.subrata-kumarSummary: The motion of the blood inside an artery is investigated under the transverse magnetic field. The velocity and temperature variation of the blood flow motion are solved by perturbation technique. We considered the magnetic field is constant and viscosity of the fluid distribution depends on temperature. We derived flow rate and wall shear stress during the flow of blood through the human artery. We analyzed the effect of temperature profiles, flow rate and wall shear stress during the propagation of blood. It is observed that the human will die with respect to the increase temperature in the blood flow distribution.Anchoring and migration of balloon in REBOAhttps://www.zbmath.org/1475.761212022-01-14T13:23:02.489162Z"Mei, C. C."https://www.zbmath.org/authors/?q=ai:mei.chiang-c"Li, Y. L."https://www.zbmath.org/authors/?q=ai:li.yile"Michele, S."https://www.zbmath.org/authors/?q=ai:michele.simone"Sammarco, P."https://www.zbmath.org/authors/?q=ai:sammarco.paolo"Mcbeth, P. B."https://www.zbmath.org/authors/?q=ai:mcbeth.p-bSummary: A mechanical theory is described for a phenomenon in the surgical procedure of resuscitative endovascular balloon occlusion of the aorta (REBOA). In this procedure a balloon is pushed into the aorta by a catheter and then inflated in order to stop haemorrhage. One of the hazards of this procedure is the tendency for the balloon to migrate away from its intended position. This work examines the mechanics of balloon anchoring and migration by analysing the effects of pressure waves, the sheet flow and solid friction in the thin gap between the walls of the aorta and balloon. A viscoelastic model is adopted for the aorta wall for pressure waves between the left ventricle and the balloon. The lubrication approximation is used for blood flow in the thin gap between the walls of the balloon and aorta. Samples of quantitative predictions are discussed on how the inflation pressure and balloon characteristics affect the balloon anchoring and migration. The crucial roles of solid friction and balloon placement are pointed out, which should help in guiding the manufacturing of balloons and their usage in the field.The protocol for using elastic wall model in modeling blood flow within human arteryhttps://www.zbmath.org/1475.761222022-01-14T13:23:02.489162Z"Nowak, Marcin"https://www.zbmath.org/authors/?q=ai:nowak.marcin"Melka, Bartłomiej"https://www.zbmath.org/authors/?q=ai:melka.bartlomiej"Rojczyk, Marek"https://www.zbmath.org/authors/?q=ai:rojczyk.marek"Gracka, Maria"https://www.zbmath.org/authors/?q=ai:gracka.maria"Nowak, Andrzej J."https://www.zbmath.org/authors/?q=ai:nowak.andrzej-jozef"Golda, Adam"https://www.zbmath.org/authors/?q=ai:golda.adam"Adamczyk, Wojciech P."https://www.zbmath.org/authors/?q=ai:adamczyk.wojciech-p"Isaac, Benjamin"https://www.zbmath.org/authors/?q=ai:isaac.benjamin"Białecki, Ryszard A."https://www.zbmath.org/authors/?q=ai:bialecki.ryszard-a"Ostrowski, Ziemowit"https://www.zbmath.org/authors/?q=ai:ostrowski.ziemowitSummary: Medical diagnostic tools will play a major role in the future for an effective patient treatment and reduction their mortality, related to the cardiovascular system diseases (CVDs). There is an urgent need for developing diagnostic procedure to be robust, reliable, accurate and efficient, in the framework of a paradigm shift. Application of numerical techniques is seen as a perspective tool for such purpose. Nevertheless, existing models need constant improvement in development robust, multi-scale models. This paper elaborates on the development of numerical model for modeling blood flow in the aorta section. The deformation of the blood vessel was modeled as two-way fluid-structure interaction (FSI) using ANSYS package. Numerical results have shown that the developed model predicts deformations of the vessels and describes their impact on the pressure, pressure drop and wall shear stresses distributions. Differences between rigid and deformed walls were checked based on pressure drop value. For movable walls, these values were higher both for systole and diastole, which is caused by the local wall compression during aforementioned moments of the cycle. The significant backflow observed during the heart cycle is connected with the deformed walls resulting in temporal blood accumulation. The maximum total deformation of the vessel walls achieved 2.35\,mm, and the difference between the maximum and minimum blood volume was equal 5.2\%.Investigation of the influence of smooth muscle contractions on the properties of the wall of a small arterial vesselhttps://www.zbmath.org/1475.761232022-01-14T13:23:02.489162Z"Shadrina, N. Kh."https://www.zbmath.org/authors/?q=ai:shadrina.n-khSummary: The plane problem of the effect of contractions of smooth muscle cells in the wall of a resistance vessel under the action of transmural pressure on the radius and the distribution of stresses in the vascular wall is considered. It is assumed that in the inactivated state the vessel wall is hyperelastic, and the contraction of smooth muscle cells as a result of activation contributes to the circumferential stress alone. Based on the model and published experimental data, a functional dependence of the active stress on the concentration of the activator of smooth muscle contraction is obtained. Calculations show that the total stress in the wall is determined mainly by the active component. With increasing pressure, contractions of smooth muscle cells lead to decrease in stresses, while the pattern of the distribution of circumferential stresses changes. The circumferential stretch ratios also decrease with activation and their distribution becomes more homogeneous. In both passive and active vessels, the modulus of the ratio of the radial to circumferential stress decreases with increase in tension, this ratio being several times greater in the active vessel than in the passive one.Second harmonic generation and vortex shedding by a dipole-quadrupole and a quadrupole-octupole swimmer in a viscous incompressible fluidhttps://www.zbmath.org/1475.761242022-01-14T13:23:02.489162Z"Felderhof, B. U."https://www.zbmath.org/authors/?q=ai:felderhof.b-u"Jones, R. B."https://www.zbmath.org/authors/?q=ai:jones.robert-b|jones.roger-bSummary: Vortex shedding by a swimming sphere in a viscous incompressible fluid is studied for surface modulation characterized by a superposition of bipolar and quadrupolar, as well as for quadrupolar and octupolar displacements, varying harmonically in time. The time-dependent swimming velocity and the flow velocity are calculated to second order in the amplitude of surface modulation for both models. The models are also useful for the discussion of bird flight.Optimal ciliary locomotion of axisymmetric microswimmershttps://www.zbmath.org/1475.761252022-01-14T13:23:02.489162Z"Guo, Hanliang"https://www.zbmath.org/authors/?q=ai:guo.hanliang"Zhu, Hai"https://www.zbmath.org/authors/?q=ai:zhu.hai"Liu, Ruowen"https://www.zbmath.org/authors/?q=ai:liu.ruowen"Bonnet, Marc"https://www.zbmath.org/authors/?q=ai:bonnet.marc"Veerapaneni, Shravan"https://www.zbmath.org/authors/?q=ai:veerapaneni.shravan-kumarSummary: Many biological microswimmers locomote by periodically beating the densely packed cilia on their cell surface in a wave-like fashion. While the swimming mechanisms of ciliated microswimmers have been extensively studied both from the analytical and the numerical point of view, optimisation of the ciliary motion of microswimmers has received limited attention, especially for non-spherical shapes. In this paper, using an envelope model for the microswimmer, we numerically optimise the ciliary motion of a ciliate with an arbitrary axisymmetric shape. Forward solutions are found using a fast boundary-integral method, and the efficiency sensitivities are derived using an adjoint-based method. Our results show that a prolate microswimmer with a \(2 : 1\) aspect ratio shares similar optimal ciliary motion as the spherical microswimmer, yet the swimming efficiency can increase two-fold. More interestingly, the optimal ciliary motion of a concave microswimmer can be qualitatively different from that of the spherical microswimmer, and adding a constraint to the cilia length is found to improve, on average, the efficiency for such swimmers.Locating the baking isotherm in a Søderberg electrode: analysis of a moving thermistor modelhttps://www.zbmath.org/1475.800042022-01-14T13:23:02.489162Z"Van Gorder, Robert A."https://www.zbmath.org/authors/?q=ai:van-gorder.robert-a"Kamilova, Alissa"https://www.zbmath.org/authors/?q=ai:kamilova.alissa"Birkeland, Rolf G."https://www.zbmath.org/authors/?q=ai:birkeland.rolf-g"Krause, Andrew L."https://www.zbmath.org/authors/?q=ai:krause.andrew-lShock wave structure for polyatomic gases with large bulk viscositieshttps://www.zbmath.org/1475.820202022-01-14T13:23:02.489162Z"Aoki, Kazuo"https://www.zbmath.org/authors/?q=ai:aoki.kazuo"Kosuge, Shingo"https://www.zbmath.org/authors/?q=ai:kosuge.shingoSummary: The structure of a standing plane shock wave in a polyatomic gas is investigated on the basis of kinetic theory, with special interest in gases with large bulk viscosities, such as \(\mathrm{CO}_2\) gas. The ellipsoidal statistical (ES) model for a polyatomic gas is employed. First, the shock structure is computed numerically for different upstream Mach numbers and for different (large) values of the ratio of the bulk viscosity to the shear viscosity, and the double-layer structure consisting of a thin upstream layer with a steep change and a much thicker downstream layer with a mild change is obtained. Then, an asymptotic analysis for large values of the ratio is carried out, and an analytical solution that describes the thick downstream layer correctly is obtained.Comparison of preconditioning strategies in energy conserving implicit particle in cell methodshttps://www.zbmath.org/1475.820262022-01-14T13:23:02.489162Z"Siddi, Lorenzo"https://www.zbmath.org/authors/?q=ai:siddi.lorenzo"Cazzola, Emanuele"https://www.zbmath.org/authors/?q=ai:cazzola.emanuele"Lapenta, Giovanni"https://www.zbmath.org/authors/?q=ai:lapenta.giovanniSummary: This work presents a set of preconditioning strategies able to significantly accelerate the performance of fully implicit energy-conserving Particle-in-Cell methods to a level that becomes competitive with semi-implicit methods. We compare three different preconditioners. We consider three methods and compare them with a straight unpreconditioned Jacobian Free Newton Krylov (JFNK) implementation. The first two focus, respectively, on improving the handling of particles (particle hiding) or fields (field hiding) within the JFNK iteration. The third uses the field hiding preconditioner within a direct Newton iteration where a Schwarz-decomposed Jacobian is computed analytically. Clearly, field hiding used with JFNK or with the direct Newton-Schwarz (DNS) method outperforms all method. We compare these implementations with a recent semi-implicit energy conserving scheme. Fully implicit methods are still lag behind in cost per cycle but not by a large margin when proper preconditioning is used. However, for exact energy conservation, preconditioned fully implicit methods are significantly easier to implement compared with semi-implicit methods and can be extended to fully relativistic physics.Optimal metric regularity in general relativity follows from the RT-equations by elliptic regularity theory in \(L^p\)-spaceshttps://www.zbmath.org/1475.830092022-01-14T13:23:02.489162Z"Reintjes, Moritz"https://www.zbmath.org/authors/?q=ai:reintjes.moritz"Temple, Blake"https://www.zbmath.org/authors/?q=ai:temple.blakeIn the paper under reviewing the authors establish the first existence theorems for the nonlinear Regularity Transformation equation (RT-equations) in the general case when
$\Gamma, Riem(\Gamma)\in W^{m,p}$ for $m\geq1, n<p<\infty$,
where $\Gamma$ is any affine connection on an $n$-dimensional manifold. From this the authors conclude that for any such connection
$\Gamma(x) \in W^{m,p}$
with
$Riem(\Gamma)\in W^{m,p}$, $m\geq1, n<p<\infty$,
given in $x$-coordinates, there always exists a coordinate transformation $x\to y$ such that
$\Gamma(x) \in W^{(m+1),p}$.
This implies all discontinuities in $m$th derivatives of $\delta\Gamma$ cancel out, the transformation $x\to y$ raises the connection regularity for the hyperbolic Einstein-Hilbert equations is thus resolved by elliptic regular theory in $L^p$-spaces applied to RT-equations.
The theorems proved apply to shock wave solutions of Einstein-Hilbert equations.
Reviewer: Alex B. Gaina (Chişinău)Relic gravitons from stiff curvature perturbationshttps://www.zbmath.org/1475.830342022-01-14T13:23:02.489162Z"Giovannini, Massimo"https://www.zbmath.org/authors/?q=ai:giovannini.massimoSummary: The tensor modes reentering the Hubble radius when the plasma is dominated by a stiff fluid lead to a spectral energy density whose blue slope depends on the total post-inflationary sound speed. This result gets however corrected by a secondary (gauge-dependent) term coming from the curvature inhomogeneities that reenter all along the same stage of expansion. In comparison with the first-order result, the secondary contribution is shown to be always suppressed inside the sound horizon and its effect on the total spectral energy density of the relic gravitons is therefore negligible for all phenomenological purposes. It is also suggested that the effective anisotropic stress of the curvature inhomogeneities can be obtained from the functional derivative of the second-order action of curvature inhomogeneities with respect to the background metric.Resonant Hawking radiation as an instabilityhttps://www.zbmath.org/1475.830542022-01-14T13:23:02.489162Z"Bermudez, David"https://www.zbmath.org/authors/?q=ai:bermudez.david"Leonhardt, Ulf"https://www.zbmath.org/authors/?q=ai:leonhardt.ulfMatter accretion onto higher-dimensional black holes with Dirac-Born-Infeld global defects via well known fluidshttps://www.zbmath.org/1475.830922022-01-14T13:23:02.489162Z"Shahzad, M. Umair"https://www.zbmath.org/authors/?q=ai:shahzad.m-umair"Ali, Rafaqat"https://www.zbmath.org/authors/?q=ai:ali.rafaqat"Jawad, Abdul"https://www.zbmath.org/authors/?q=ai:jawad.abdulSummary: In this paper, we analyze the matter accretion onto higher dimensional black holes with Dirac-Born-Infeld (DBI) global defects by assuming general form of the recently proposed Hamiltonian and dynamical system for the fluid by considering the steady state flow. It is possible to obtain the analytic solution for isothermal equation of state and observe the heteroclinic flow in the presence of well-known fluids such as ultra-stiff, radiation, sub-relativistic and ultra-relativistic. A homoclinic-type accretion flow is observed for polytropic test fluid and the behavior for the adiabatic index \(1 < \beta = 5 / 3 < 2\) and \(\beta = 7 / 3 > 2\) is discussed. In addition, we investigate the behavior of energy density, radial velocity and mass accretion rate onto higher dimensional black holes with DBI global defects in the presence of above mentioned fluids.Radial oscillations of boson stars made of ultralight repulsive dark matterhttps://www.zbmath.org/1475.850092022-01-14T13:23:02.489162Z"Lopes, Ilídio"https://www.zbmath.org/authors/?q=ai:lopes.ilidio"Panotopoulos, Grigoris"https://www.zbmath.org/authors/?q=ai:panotopoulos.grigorisSummary: We compute the lowest frequency radial oscillation modes of boson stars. It is assumed that the object is made of pseudo-Goldstone bosons subjected to a scalar potential that leads to a repulsive self-interaction force, and which is characterized by two unknown mass scales \(m\) (mass of the particle) and \(F\) (decay constant). First we integrate the Tolman-Oppenheimer-Volkoff equations for the hydrostatic equilibrium of the star, and then we solve the Sturm-Liouville boundary value problem for the perturbations using the shooting method. The effective potential that enters into the Schrödinger-like equation as well as several associated eigenfunctions are shown as well. Moreover, we found that the large frequency separation, i.e. the difference between consecutive modes, is proportional to the square root of the mass of the star and the cube of the mass scale defined by \(\Lambda \equiv \sqrt{mF} \).Thermal vorticity and thermal chirality in relativistic thermally conducting fluidhttps://www.zbmath.org/1475.850112022-01-14T13:23:02.489162Z"Prasad, G."https://www.zbmath.org/authors/?q=ai:prasad.girijesh|prasad.g-s|prasad.g-v|prasad.gopal|prasad.gunray|prasad.gunraj|prasad.govind|prasad.gopi|prasad.g-b-k-sPulsation flow of incompressible electrically conducting liquid with heat transferhttps://www.zbmath.org/1475.850152022-01-14T13:23:02.489162Z"Sharikadze, J."https://www.zbmath.org/authors/?q=ai:sharikadze.j"Tsutskiridze, V."https://www.zbmath.org/authors/?q=ai:tsutskiridze.v-n|tsutskiridze.varden"Jikidze, L."https://www.zbmath.org/authors/?q=ai:jikidze.levan|jikidze.l-aSummary: It is considered pulsating flow of electro-conductive viscous incompressible liquid between two parallel walls, which is caused by drop of pulsative pressure and but pulsative motion of walls when external homogeneous magnetic field acts perpendicularly to the walls.Numerical solution of traffic flow modelshttps://www.zbmath.org/1475.900042022-01-14T13:23:02.489162Z"Vacek, Lukáš"https://www.zbmath.org/authors/?q=ai:vacek.lukas"Kučera, Václav"https://www.zbmath.org/authors/?q=ai:kucera.vaclavSummary: We describe the simulation of traffic flows on networks. On individual roads we use standard macroscopic traffic models. The discontinuous Galerkin method in space and a multistep method in time is used for the numerical solution. We introduce limiters to keep the density in an admissible interval as well as prevent spurious oscillations in the numerical solution. To simulate traffic on networks, one should construct suitable numerical fluxes at junctions.
For the entire collection see [Zbl 1471.65009].Complete transition diagrams of generic Hamiltonian flows with a few heteroclinic orbitshttps://www.zbmath.org/1475.901212022-01-14T13:23:02.489162Z"Yokoyama, Tetsuo"https://www.zbmath.org/authors/?q=ai:yokoyama.tetsuo"Yokoyama, Tomoo"https://www.zbmath.org/authors/?q=ai:yokoyama.tomooBiofluid mechanics. Analysis and applicationshttps://www.zbmath.org/1475.920022022-01-14T13:23:02.489162Z"Grotberg, James B."https://www.zbmath.org/authors/?q=ai:grotberg.james-bPublisher's description: Condensing 40 years of teaching experience, this unique textbook will provide students with an unrivalled understanding of the fundamentals of fluid mechanics, and enable them to place that understanding firmly within a biological context. Each chapter introduces, explains, and expands a core concept in biofluid mechanics, establishing a firm theoretical framework for students to build upon in further study. Practical biofluid applications, clinical correlations, and worked examples throughout the book provide real-world scenarios to help students quickly master key theoretical topics. Examples are drawn from biology, medicine, and biotechnology with applications to normal function, disease, and devices, accompanied by over 500 figures to reinforce student understanding. Featuring over 120 multicomponent end-of-chapter problems, flexible teaching pathways to enable tailor-made course structures, and extensive Matlab and Maple code examples, this is the definitive textbook for advanced undergraduate and graduate students studying a biologically-grounded course in fluid mechanics.Mathematical and numerical models of atherosclerotic plaque progression in carotid arterieshttps://www.zbmath.org/1475.920102022-01-14T13:23:02.489162Z"Pozzi, Silvia"https://www.zbmath.org/authors/?q=ai:pozzi.silvia"Vergara, Christian"https://www.zbmath.org/authors/?q=ai:vergara.christianSummary: We propose a mathematical model for the description of plaque progression in carotid arteries. This is based on the coupling of a fluid-structure interaction problem, arising between blood and vessel wall, and differential problems for the cellular evolution. A numerical model is also proposed. This is based on the splitting of the coupled problem based on a suitable strategy to manage the multiscale-in-time nature of the problem. We present some preliminary numerical results both in ideal and real scenarios.
For the entire collection see [Zbl 1471.65009].Revealing the actions of the human cochlear basilar membrane at low frequencyhttps://www.zbmath.org/1475.920282022-01-14T13:23:02.489162Z"Yao, Wenjuan"https://www.zbmath.org/authors/?q=ai:yao.wenjuan"Liang, Junyi"https://www.zbmath.org/authors/?q=ai:liang.junyi"Ren, Liujie"https://www.zbmath.org/authors/?q=ai:ren.liujie"Ma, Jianwei"https://www.zbmath.org/authors/?q=ai:ma.jianwei"Zhao, Zhengshan"https://www.zbmath.org/authors/?q=ai:zhao.zhengshan"Wang, Jiakun"https://www.zbmath.org/authors/?q=ai:wang.jiakun"Xie, Youzhou"https://www.zbmath.org/authors/?q=ai:xie.youzhou"Dai, Peidong"https://www.zbmath.org/authors/?q=ai:dai.peidong"Zhang, Tianyu"https://www.zbmath.org/authors/?q=ai:zhang.tianyuSummary: The basilar membrane (BM) is the key infrastructure that supports the microstructure of cochlear acoustic function, and its interaction with lymph in the cochlea involves a complex, highly nonlinear coupling motion and energy conversion. In 1928, Nobel Laureate Gordon von Békésy experimented and first discovered the traveling wave motion of the BM, thus uncovering the mystery of BM motion. However, with the further development of experimental technology in recent years, scientists have discovered that the traveling wave motion does not explain many experimental observations and phenomena associated with the detection of low-frequency sounds by the cochlea. Because the cochlea is very small and complex, Békésy could only obtain medium- and high-frequency motion data for the BM but not low-frequency motion data. Based on a theory of mathematical physics and biology combined with data from medical and modern light source imaging experiments, a theoretical model of the spiral cochlea and a numerical model that conforms to the real human ear were established. The results reproduce the known traveling wave motion of the BM. Meanwhile, an exciting new finding has revealed a standing wave motion pattern at low frequencies. This newly discovered motion pattern intrinsically explains many experimental observations that could not be explained by the traveling wave theory. These results not only complement the low-frequency motion characteristics of the BM, but also probably reveal the mechanism of active phonoreceptive amplification in the cochlea, which has been a difficult problem to unravel in otology medicine.Mathematical modeling of embolization of arteriovenous malformations with overflows on the basis of the two-phase filteringhttps://www.zbmath.org/1475.920622022-01-14T13:23:02.489162Z"Gologush, T. S."https://www.zbmath.org/authors/?q=ai:gologush.t-s"Ostapenko, V. V."https://www.zbmath.org/authors/?q=ai:ostapenko.vladimir-v"Cherevko, A. A."https://www.zbmath.org/authors/?q=ai:cherevko.alexander-aSummary: Arteriovenous malformation (AVM) is a congenital pathology of the development of brain vessels in which the arterial and venous blood beds are directly connected by tangled degenerate vessels. This dangerous disease affects the brain functioning and increasing the risk of intracranial hemorrhage. A method of treating the AVM is embolization, which is the surgery of endovascular filling of AVM vessels by a special embolic agent to block blood flow through them. This method is widely used; however, it sometimes is accompanied by intraoperative rupture of AVM vessels. A combined model of the embolization process is proposed that, in addition to the flow of blood and embolic agent in the AVM, takes into account the overflow of blood into surrounding healthy vessels. For modeling the joint flow of blood and embolic composition within the AVM, a one-dimensional model of two-phase filtering is used. This model is built on the basis of clinical data of real patients obtained during neurosurgeries in the Meshalkin National Medical Research Center. Mathematically, this leads to a special initial boundary value problem for an integro-differential equation with a nonconvex flow. For numerical computations, a monotone modification of the CABARET scheme is constructed that highly accurately localizes the strong and weak discontinuities in the solution to the problem. The main purpose of this paper is to find the optimal scenario of the AVM embolization with respect to safety and efficiency. The objective functional and the constraints occurring in the resulting optimal control problem are chosen according to medical grounds. In the future, it is planned to use the optimal solutions obtained in this paper to improve the surgery technique and increase the safety of neurosurgical operations.Energy-based fluid-structure model of the vocal foldshttps://www.zbmath.org/1475.920632022-01-14T13:23:02.489162Z"Mora, Luis A."https://www.zbmath.org/authors/?q=ai:mora.luis-a"Ramirez, Hector"https://www.zbmath.org/authors/?q=ai:ramirez.hector-c"Yuz, Juan I."https://www.zbmath.org/authors/?q=ai:yuz.juan-i"Le Gorec, Yann"https://www.zbmath.org/authors/?q=ai:le-gorec.yann"Zañartu, Matías"https://www.zbmath.org/authors/?q=ai:zanartu.matiasSummary: Lumped elements models of vocal folds are relevant research tools that can enhance the understanding of the pathophysiology of many voice disorders. In this paper, we use the port-Hamiltonian framework to obtain an energy-based model for the fluid-structure interactions between the vocal folds and the airflow in the glottis. The vocal fold behavior is represented by a three-mass model and the airflow is described as a fluid with irrotational flow. The proposed approach allows to go beyond the usual quasi-steady one-dimensional flow assumption in lumped mass models. The simulation results show that the proposed energy-based model successfully reproduces the oscillations of the vocal folds, including the collision phenomena, and it is useful to analyze the energy exchange between the airflow and the vocal folds.A multi-scale flow model for studying blood circulation in vascular systemhttps://www.zbmath.org/1475.920642022-01-14T13:23:02.489162Z"Qohar, Ulin Nuha Abdul"https://www.zbmath.org/authors/?q=ai:qohar.ulin-nuha-abdul"Munthe-Kaas, Antonella Zanna"https://www.zbmath.org/authors/?q=ai:zanna-munthe-kaas.antonella"Nordbotten, Jan Martin"https://www.zbmath.org/authors/?q=ai:nordbotten.jan-martin"Hanson, Erik Andreas"https://www.zbmath.org/authors/?q=ai:hanson.erik-andreasSummary: In this paper, we demonstrate a multi-scale model for studying blood flow in the vascular structures of an organ. The model may be used for a tracer concentration flow simulation replicating Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) data. A 1D vascular graph model that represents blood flow through a vascular vessel network is coupled with a single-phase Darcy flow model for the capillary bed which is assumed as a porous media. Numerical experiments show the blood circulation in the system closely related to the structure and parameter of the vascular system, that gives qualitatively realistic tracer concentration flow. This model is a starting point for further investigation in development into clinical applications, using both real data and MRI analysis software.
For the entire collection see [Zbl 1471.65009].Hydrodynamic limit of a coupled Cucker-Smale system with strong and weak internal variable relaxationhttps://www.zbmath.org/1475.922182022-01-14T13:23:02.489162Z"Kim, Jeongho"https://www.zbmath.org/authors/?q=ai:kim.jeongho"Poyato, David"https://www.zbmath.org/authors/?q=ai:poyato.david"Soler, Juan"https://www.zbmath.org/authors/?q=ai:soler.juan-s