Recent zbMATH articles in MSC 76Thttps://www.zbmath.org/atom/cc/76T2021-04-16T16:22:00+00:00WerkzeugMethodology for the numerical study of the methane hydrate formation during gas injection into a porous medium.https://www.zbmath.org/1456.760842021-04-16T16:22:00+00:00"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-leonidovich"Gubaidullin, A. A."https://www.zbmath.org/authors/?q=ai:gubaidullin.a-aSummary: Mathematical model is proposed that describes the process of pumping gas into a porous medium initially filled with methane and water. Non-ideal gas and non-isothermal effects during its filtration are taken into account. The hydrate formation process is assumed to be equilibrium. Methodology for solving the system of equations of the mathematical model is constructed. The methodology was tested, in the one-dimensional axisymmetric case the calculation results were compared with a self-similar solution for a perfect gas, which showed a good qualitative and quantitative agreement.Corrector equations in fluid mechanics: effective viscosity of colloidal suspensions.https://www.zbmath.org/1456.761342021-04-16T16:22:00+00:00"Duerinckx, Mitia"https://www.zbmath.org/authors/?q=ai:duerinckx.mitia"Gloria, Antoine"https://www.zbmath.org/authors/?q=ai:gloria.antoineSummary: Consider a colloidal suspension of rigid particles in a steady Stokes flow. In a celebrated work, Einstein argued that in the regime of dilute particles the system behaves at leading order like a Stokes fluid with some explicit effective viscosity. In the present contribution, we rigorously define a notion of effective viscosity, regardless of the dilute regime assumption. More precisely, we establish a homogenization result for when particles are distributed according to a given stationary and ergodic random point process. The main novelty is the introduction and analysis of suitable corrector equations.Interfacial structure of water/methanol mixture in contact with graphene surface using molecular dynamics simulation.https://www.zbmath.org/1456.761362021-04-16T16:22:00+00:00"Safaei, Nehzat"https://www.zbmath.org/authors/?q=ai:safaei.nehzat"Maghari, Ali"https://www.zbmath.org/authors/?q=ai:maghari.aliThe oblique fall of an acoustic wave on the boundary of a multifractional gas suspension with polydisperse inclusions.https://www.zbmath.org/1456.761152021-04-16T16:22:00+00:00"Gubaidullin, D. A."https://www.zbmath.org/authors/?q=ai:gubaidullin.d-a"Zaripov, R. R."https://www.zbmath.org/authors/?q=ai:zaripov.r-rSummary: This article is devoted to the study of the oblique fall of an acoustic wave from a pure gas to the boundary of a multifraction gas suspension with polydisperse inclusions of different sizes and materials. A mathematical model that allows to determine the reflection coefficient when an acoustic wave falls obliquely on the interface between two media is presented. Dependencies of the reflection coefficient on the disturbance frequency were calculated. Influence of the oblique angle of acoustic wave on the dependence of the reflection coefficient was established.The influence of boundary temperatures and concentrations jumps on the evaporating spheroidal drop in moderately rare binary gas mixture.https://www.zbmath.org/1456.761292021-04-16T16:22:00+00:00"D'yakonov, S. N."https://www.zbmath.org/authors/?q=ai:dyakonov.s-n"Ryumshin, B. V."https://www.zbmath.org/authors/?q=ai:ryumshin.b-vSummary: The ihfluence of boundary temperatures and concentrations jumps on the evaporating spheroidal drop in moderately rare binary gas mixture.A unified lattice Boltzmann model for immiscible and miscible ternary fluids.https://www.zbmath.org/1456.760932021-04-16T16:22:00+00:00"He, Qiang"https://www.zbmath.org/authors/?q=ai:he.qiang"Li, Yongjian"https://www.zbmath.org/authors/?q=ai:li.yongjian"Huang, Weifeng"https://www.zbmath.org/authors/?q=ai:huang.weifeng"Hu, Yang"https://www.zbmath.org/authors/?q=ai:hu.yang"Li, Decai"https://www.zbmath.org/authors/?q=ai:li.decai"Wang, Yuming"https://www.zbmath.org/authors/?q=ai:wang.yumingSummary: Based on the phase-field theory, we develop a unified lattice Boltzmann model for ternary flow, in which the miscibility between the three fluid components can be adjusted independently. Based on a modified free energy function, we derive the conservative phase-field equations using the gradient flow method. A generalized continuous surface tension force formulation is deduced by using the virtual work method. The wetting boundary condition is derived based on mass conservation law. The proposed model for ternary fluids is consistent with the binary-fluid models in the absence of one fluid. A lattice Boltzmann (LB) model is developed to solve the phase-field equations and hydrodynamic equations, and this model can deal with problems involving high density and viscosity contrasts. The proposed method is examined through several test cases. A layered Poiseuille flow and droplet coalescence problems are carried out to validate the present LB model. Several dynamic problems in ternary fluid problems involving a solid are simulated, including the wetting of two droplets on a circular cylinder and impacting of a multiphase droplet on a fixed particle. Finally, we apply the model to a three-dimensional multi-bubbles rising problem to access its numerical accuracy and stability.A two-dimensional VOF interface reconstruction in a multi-material cell-centered ALE scheme.https://www.zbmath.org/1456.761002021-04-16T16:22:00+00:00"Breil, Jérôme"https://www.zbmath.org/authors/?q=ai:breil.jerome"Galera, Stéphane"https://www.zbmath.org/authors/?q=ai:galera.stephane"Maire, Pierre-Henri"https://www.zbmath.org/authors/?q=ai:maire.pierre-henriSummary: We present an original and accurate cell-centered ALE (arbitrary Lagrangian-Eulerian) algorithm devoted to the simulation of multi-material fluid flows using VOF (Volume Of Fluid) interface reconstruction.Adaptive methods for multi-material ALE hydrodynamics.https://www.zbmath.org/1456.761062021-04-16T16:22:00+00:00"Rider, W. J."https://www.zbmath.org/authors/?q=ai:rider.william-j"Love, E."https://www.zbmath.org/authors/?q=ai:love.edward|love.ernie|love.elizabeth|love.eric-russell"Wong, M. K."https://www.zbmath.org/authors/?q=ai:wong.michael-k"Strack, O. E."https://www.zbmath.org/authors/?q=ai:strack.o-erik"Petney, S. V."https://www.zbmath.org/authors/?q=ai:petney.s-v"Labreche, D. A."https://www.zbmath.org/authors/?q=ai:labreche.d-aSummary: Arbitrary Lagrangian-Eulerian (ALE) methods are commonly used for challenging problems in hydrodynamics. Among the most challenging matters are the approximations in the presence of multiple materials. The ALE code ALEGRA has used a constant volume method for computing the impact of multiple materials on both the Lagrangian step and the remap step of the method. Here, we describe modifications to these methods that provide greater modeling fidelity and better numerical and computational performance. In the Lagrangian step, the effects of differences in material response were not included in the constant volume method, but have been included in the new method. The new methodology can produce unstable results unless the changes in the variable states are carefully controlled. Both the stability analysis and the control of the instability are described. In the standard (Van Leer) method for the remap, the numerical approximation did not account for the presence of a material interface directly. The new methodology uses different, more stable and more dissipative numerical approximations in and near material interfaces. In addition, the standard numerical method, which is second-order accurate, has been replaced by a more accurate method, which is third-order accurate in one dimension.A monotonicity-preserving higher-order accurate finite-volume method for Kapila's two-fluid flow model.https://www.zbmath.org/1456.760772021-04-16T16:22:00+00:00"de Böck, R."https://www.zbmath.org/authors/?q=ai:de-bock.r"Tijsseling, A. S."https://www.zbmath.org/authors/?q=ai:tijsseling.arris-s"Koren, B."https://www.zbmath.org/authors/?q=ai:koren.barrySummary: In preparation of the study of liquefied natural gas (LNG) sloshing in ships and vehicles, we model and numerically analyze compressible two-fluid flow. We consider a five-equation two-fluid flow model, assuming velocity and pressure continuity across two-fluid interfaces, with a separate equation to track the interfaces. The system of partial differential equations is hyperbolic and quasi-conservative. It is discretized in space with a tailor-made third-order accurate finite-volume method, employing an HLLC approximate Riemann solver. The third-order accuracy is obtained through spatial reconstruction with a limiter function, for which a novel formulation is presented. The non-homogeneous term is handled in a way consistent with the HLLC treatment of the convection operator. We study the one-dimensional case of a liquid column impacting onto a gas pocket entrapped at a solid wall. It mimics the impact of a breaking wave in an LNG containment system, where a gas pocket is entrapped at the tank wall below the wave crest. Furthermore, the impact of a shock wave on a gas bubble containing the heavy gas R22, immersed in air, is simulated in two dimensions and compared with experimental results. The numerical scheme is shown to be higher-order accurate in space and capable of capturing the important characteristics of compressible two-fluid flow.Towards an \(H\)-theorem for granular gases.https://www.zbmath.org/1456.828172021-04-16T16:22:00+00:00"García de Soria, María Isabel"https://www.zbmath.org/authors/?q=ai:de-soria.maria-isabel-garcia"Maynar, Pablo"https://www.zbmath.org/authors/?q=ai:maynar.pablo"Mischler, Stéphane"https://www.zbmath.org/authors/?q=ai:mischler.stephane"Mouhot, Clément"https://www.zbmath.org/authors/?q=ai:mouhot.clement"Rey, Thomas"https://www.zbmath.org/authors/?q=ai:rey.thomas"Trizac, Emmanuel"https://www.zbmath.org/authors/?q=ai:trizac.emmanuelBubble pinch-off in turbulence.https://www.zbmath.org/1456.761312021-04-16T16:22:00+00:00"Ruth, Daniel J."https://www.zbmath.org/authors/?q=ai:ruth.daniel-j"Mostert, Wouter"https://www.zbmath.org/authors/?q=ai:mostert.wouter"Perrard, Stéphane"https://www.zbmath.org/authors/?q=ai:perrard.stephane"Deike, Luc"https://www.zbmath.org/authors/?q=ai:deike.lucSummary: Although bubble pinch-off is an archetype of a dynamical system evolving toward a singularity, it has always been described in idealized theoretical and experimental conditions. Here, we consider bubble pinch-off in a turbulent flow representative of natural conditions in the presence of strong and random perturbations, combining laboratory experiments, numerical simulations, and theoretical modeling. We show that the turbulence sets the initial conditions for pinch-off, namely the initial bubble shape and flow field, but after the pinch-off starts, the turbulent time at the neck scale becomes much slower than the pinching dynamics: The turbulence freezes. We show that the average neck size, \( \overline{d} \), can be described by \(\overline{d} \sim ( t - t_0 )^\alpha \), where \(t_0\) is the pinch-off or singularity time and \(\alpha \approx 0.5\), in close agreement with the axisymmetric theory with no initial flow. While frozen, the turbulence can influence the pinch-off through the initial conditions. Neck shape oscillations described by a quasi-2-dimensional (quasi-2D) linear perturbation model are observed as are persistent eccentricities of the neck, which are related to the complex flow field induced by the deformed bubble shape. When turbulent stresses are less able to be counteracted by surface tension, a 3-dimensional (3D) kink-like structure develops in the neck, causing \(\overline{d}\) to escape its self-similar decrease. We identify the geometric controlling parameter that governs the appearance of these kink-like interfacial structures, which drive the collapse out of the self-similar route, governing both the likelihood of escaping the self-similar process and the time and length scale at which it occurs.Nanofluid bio-thermal convection: simultaneous effects of gyrotactic and oxytactic micro-organisms.https://www.zbmath.org/1456.760492021-04-16T16:22:00+00:00"Kuznetsov, A. V."https://www.zbmath.org/authors/?q=ai:kuznetsov.alex-v|kuznetsov.andrey-v|kuznetsov.aleksandr-vOn traveling waves in compressible Euler equations with thermal conductivity.https://www.zbmath.org/1456.350702021-04-16T16:22:00+00:00"Thanh, Mai Duc"https://www.zbmath.org/authors/?q=ai:mai-duc-thanh."Vinh, Duong Xuan"https://www.zbmath.org/authors/?q=ai:vinh.duong-xuanSummary: Heat conduction plays an important role in fluid dynamics. However, the modeling of thermal conductivity involves higher order derivatives which causes a tough obstacle for the study of traveling waves. In this work, we propose a modified term for the thermal conductivity coefficient in viscous-capillary compressible Euler equations. By approximation, which is crucial in any mathematical modeling, the heat conduction may be assumed to depend only on the specific volume. Then, we can derive a \(2\times 2\) system of first-order differential equations for traveling waves of the given model, whose equilibria can be shown to admit a stable-saddle connection for 1-shocks and a saddle-stable connection for 3-shocks. This establishes the existence of a traveling wave of the viscous-capillary Euler equations with the presence of a modified thermal conductivity effect.Mathematical modelling of evaporating droplets dynamics in a vortex ring using moment method.https://www.zbmath.org/1456.761012021-04-16T16:22:00+00:00"Gilfanov, A. K."https://www.zbmath.org/authors/?q=ai:gilfanov.a-k"Salahov, R. R."https://www.zbmath.org/authors/?q=ai:salahov.r-r"Zaripov, T. S."https://www.zbmath.org/authors/?q=ai:zaripov.t-sSummary: The quadrature method of moments (QMOM) and method of moments with a lognormal particle size distribution (PSD) are applied to simulate a cloud of evaporating droplets in a vortex ring flow. Results predicted by both methods are compared for the cases with a sinusoidal and lognormal initial particle size distribution, using Lagrangian particle tracking as a reference solution. Spatial distributions of droplet number density obtained by different methods are shown to be in a qualitative agreement. The method of moments with a lognormal PSD overestimates disappearance of particles leading to the underestimation of droplet mean size and higher values of the variance of PSD. QMOM showed better agreement with the Lagrangian approach than the method of moments with a lognormal PSD.Homogeneous steady states in a granular fluid driven by a stochastic bath with friction.https://www.zbmath.org/1456.828132021-04-16T16:22:00+00:00"Chamorro, Moisés G."https://www.zbmath.org/authors/?q=ai:chamorro.moises-g"Vega Reyes, Francisco"https://www.zbmath.org/authors/?q=ai:vega-reyes.francisco"Garzó, Vicente"https://www.zbmath.org/authors/?q=ai:garzo.vicenteOn wells modeling in filtration problems.https://www.zbmath.org/1456.650702021-04-16T16:22:00+00:00"Ivanov, Maksim I."https://www.zbmath.org/authors/?q=ai:ivanov.maksim-i"Kremer, Igor' A."https://www.zbmath.org/authors/?q=ai:kremer.igor-a"Laevskiĭ, Yuriĭ M."https://www.zbmath.org/authors/?q=ai:laevskii.yurii-mironovichSummary: The work is devoted to one of the approaches of wells modeling within numerical oil reservoir simulation. The approach can be consider as fictitious domain method at mixed finite element approximation, which is used for non-stationary filtration processes of two phase fluid in Bukley-Leverett problem. The numerical results are compared with the results for the problem with usual Neumann conditions at the wells boundaries.Fluctuations in the uniform shear flow state of a granular gas.https://www.zbmath.org/1456.828182021-04-16T16:22:00+00:00"García de Soria, M. I."https://www.zbmath.org/authors/?q=ai:garcia-de-soria.m-i"Maynar, P."https://www.zbmath.org/authors/?q=ai:maynar.pablo"Brey, J. Javier"https://www.zbmath.org/authors/?q=ai:brey.j-javierEffect of surfactant on motion and deformation of compound droplets in arbitrary unbounded Stokes flows.https://www.zbmath.org/1456.761302021-04-16T16:22:00+00:00"Mandal, Shubhadeep"https://www.zbmath.org/authors/?q=ai:mandal.shubhadeep"Ghosh, Uddipta"https://www.zbmath.org/authors/?q=ai:ghosh.uddipta"Chakraborty, Suman"https://www.zbmath.org/authors/?q=ai:chakraborty.sumanSummary: This study deals with the motion and deformation of a compound drop system, subject to arbitrary but Stokesian far-field flow conditions, in the presence of bulk-insoluble surfactants. We derive solutions for fluid velocities and the resulting surfactant concentrations, assuming the capillary number and surface Péclet number to be small, as compared with unity. We first focus on a concentric drop configuration and apply Lamb's general solution, assuming the far-field flow to be arbitrary in nature. As representative case studies, we consider two cases: (i) flow dynamics in linear flows and (ii) flow dynamics in a Poiseuille flow, although for the latter case, the concentric configuration does not remain valid in general. We further look into the effective viscosity of a dilute suspension of compound drops, subject to linear ambient flow, and compare our predictions with previously reported experiments. Subsequently, the eccentric drop configuration is addressed by using a bipolar coordinate system where the far-field flow is assumed to be axisymmetric but otherwise arbitrary in nature. As a specific example for eccentric drop dynamics, we focus on Poiseuille flow and study the drop migration velocities. Our analysis shows that the presence of surfactant generally opposes the imposed flows, thereby acting like an effective augmented viscosity. Our analysis reveals that maximizing the effects of surfactant makes the drops behave like solid particles suspended in a medium. However, in uniaxial extensional flow, the presence of surfactants on the inner drop, in conjunction with the drop radius ratio, leads to a host of interesting and non-monotonic behaviours for the interface deformation. For eccentric drops, the effect of eccentricity only becomes noticeable after it surpasses a certain critical value, and becomes most prominent when the two interfaces approach each other. We further depict that surfactant and eccentricity generally tend to suppress each other's effects on the droplet migration velocities.A class of Lagrangian-Eulerian shock-capturing schemes for first-order hyperbolic problems with forcing terms.https://www.zbmath.org/1456.650562021-04-16T16:22:00+00:00"Abreu, E."https://www.zbmath.org/authors/?q=ai:abreu.eduardo|abreu.emerson-a-m|abreu.everton-m-c"Matos, V."https://www.zbmath.org/authors/?q=ai:matos.vitor|matos.vinicius-bitencourt"Pérez, J."https://www.zbmath.org/authors/?q=ai:perez.jorge-e|perez.j-jones|perez.jaime-castillo|perez-aparicio.jose-l|perez.jesus-hernando|perez.jose-philippe|perez.josep-m|perez.joaquin.1|perez.jose-n|perez.jose-miguel|perez.joaquin|perez.joe-j|perez.jezabel|perez.javier-j|perez.jerome|perez.jonathan|perez.jorge-a|perez.jose-antonio|perez.jesus-carretero|perez-jimenez.juan-de-dios|perez.jose-a-moreno|perez.juan-carlos|perez.jon|perez.juan-f|perez.jose-maria|perez.j-fernando|perez.juan-j|perez.johanna-camargo|perez.joshue|perez.jhon-jairo|perez.julien|perez.juan-antonio-navarro|perez.john|perez.juan-luis|perez.juan-manuel|perez.jose-luis|perez.jaime-a-moreno|perez.jesus-m|perez.jennifer|perez-garmendia.jose-luis|perez.joel"Rodríguez-Bermúdez, P."https://www.zbmath.org/authors/?q=ai:rodriguez-bermudez.pantersSummary: In this work, we develop an improved shock-capturing and high-resolution Lagrangian-Eulerian method for hyperbolic systems and balance laws. This is a new method to deal with discontinuous flux and complicated source terms having concentrations for a wide range of applications science and engineering, namely, 1D shallow-water equations, sedimentation processes, Geophysical flows in 2D, N-Wave models, and Riccati-type problems with forcing terms. We also include numerical simulations of a 1D two-phase flow model in porous media, with gravity and a nontrivial singular \(\delta\)-source term representing an injection point. Moreover, we present approximate solutions for 2D nonlinear systems (Compressible Euler Flows and Shallow-Water Equations) for distinct benchmark configurations available in the literature aiming to present convincing and robust numerical results. In addition, for the linear advection model in 1D and for a smooth solution of the nonlinear Burgers' problem, second order approximations were obtained. We also present a high-resolution approximation of the nonlinear non-convex Buckley-Leverett problem. Based on the work of A. Harten, we derive a convergent Lagrangian-Eulerian scheme that is total variation diminishing and second-order accurate, away from local extrema and discontinuous data. Additionally, using a suitable Kružkov's entropy definition, introduced by K. H. Karlsen and J. D. Towers, we can verify that our improved Lagrangian-Eulerian scheme converges to the unique entropy solution for conservation laws with a discontinuous space-time dependent flux. A key hallmark of our method is the dynamic tracking forward of the no-flow curves, which are locally conservative and preserve the natural setting of weak entropic solutions related to hyperbolic problems that are not reversible systems in general. In the end, we have a general procedure to construct a class of Lagrangian-Eulerian schemes to deal with hyperbolic problems with or without forcing terms. The proposed scheme is free of Riemann problem solutions and no adaptive space-time discretizations are needed. The numerical experiments verify the efficiency and accuracy of our new Lagrangian-Eulerian method.Modulation of solitary waves and formation of stable attractors in granular scalar models subjected to on-site perturbation.https://www.zbmath.org/1456.740972021-04-16T16:22:00+00:00"Ben-Meir, Y."https://www.zbmath.org/authors/?q=ai:ben-meir.y"Starosvetsky, Y."https://www.zbmath.org/authors/?q=ai:starosvetsky.yuliSummary: Present work concerns the propagation of solitary waves in the array of coupled, uncompressed granular chains subjected to onsite perturbation. We devise a special analytical procedure depicting the modulation of solitary pulses caused by the inter-chain interaction as well as by the on-site perturbations of a general type. The proposed analytical procedure is very efficient in depicting both the transient response characterized by significant energy fluctuations between the chains as well as in predicting the formation of stable attractors corresponding to a steady state response. We confirm the validity of a general analytical procedure with several specific setups of granular scalar models. In particular we consider the response of the array of coupled granular chains free of perturbation as well as the arrays subject to the basic type of on-site perturbations such as the ones induced by the uniform and random elastic foundation, dissipation. Additional interesting finding made in the present study corresponds to the granular arrays subject to a special type of on-site perturbation containing the terms leading to the two opposing effects namely dissipation and energy sourcing. Interestingly enough this type of perturbation may lead to the formation of stable attractors. By the term attractors we refer to the stable, stationary pulses simultaneously forming on all the coupled chains and propagating with the same phase speed. It is important to emphasize that the analytical procedure developed in the first part of the study predicts the formation of stable attractors through a typical saddle-node bifurcation. Moreover, results of the reduced model are found to be in a spectacular agreement with those of the direct numerical simulations of the true model.Transport between two fluids across their mutual flow interface: the streakline approach.https://www.zbmath.org/1456.761282021-04-16T16:22:00+00:00"Balasuriya, Sanjeeva"https://www.zbmath.org/authors/?q=ai:balasuriya.sanjeevaInteraction between free surface flow and moving bodies with a dynamic mesh and interface geometric reconstruction approach.https://www.zbmath.org/1456.761032021-04-16T16:22:00+00:00"Li, Ming-Jian"https://www.zbmath.org/authors/?q=ai:li.mingjianSummary: To investigate the fluid-rigid body interaction issues with free surfaces, a numerical approach has been developed. This algorithm is in an arbitrary Lagrangian-Eulerian description and Volume of Fluid (VOF) framework, using dynamic unstructured mesh to solve the coupled system. The fluid-solid interface uses partitioned Dirichlet-Neumann iterations with Aitken's relaxation. For the two-phase fluids part, an interface geometric reconstruction approach has been applied to accurately capture the free surfaces. This piecewise linear interface calculation (PLIC) based method uses Newton's iteration to efficiently reconstruct interfaces on an unstructured mesh, and applies an un-split scheme to transport variables. The algorithm has been successfully implemented in open source code OpenFOAM\(^{\circledR}\), and was compared with the latter's built-in solver using interface compression method to deal with free surfaces. Numerical results suggest that our solver has better accuracy on multiphase flow problems, while the previous solver fails to obtain correct interfaces. Moreover, the capacity of accurately solving fluid-rigid body interaction problems with free surfaces has been achieved. Validation cases are provided for fluid-structure interaction problems with and without free surfaces, and results are in accordance with analytical and experimental data from the literature. The algorithm and solver in this paper, can be applied on fluid-structure interaction cases with free surfaces in the future, such as sloshing and water entry problems.Improvements on bed-shear stress formulation for pier scour computation.https://www.zbmath.org/1456.761322021-04-16T16:22:00+00:00"Abbasnia, Amir Hosein"https://www.zbmath.org/authors/?q=ai:abbasnia.amir-hosein"Ghiassi, Reza"https://www.zbmath.org/authors/?q=ai:ghiassi.rezaSummary: This paper introduces an improved formula for the bed-shear stress by applying the vorticity effect and its application in a 3D flow and sediment model to estimate scouring around bridge piers. Up to now, the sediment transport formulae used for computing pier scour were developed based on the general scouring in unobstructed flow. The capability for numerical models to predict local scour around bridge piers was severely restricted by the sediment transport formulae. The new formula introduced in this paper can take into account vortices that affect the local scour process by adding some terms into the classic bed-shear stress equation.
The 3D numerical model system used in this study consists of three modules: (a) an unsteady hydrodynamic module; (b) a sediment transport module; and (c) a Fation module. The hydrodynamic module is based on the 3D RANS equations. The sediment transport module is comprised of semi empirical models of suspended load and non-equilibrium bed load. The bed-deformation module is based on the mass balance for sediment.
The model was used to simulate pier scour in tree different test cases: (1) a circular pier; (2) a square pier; and (3) a rectangular pier, by applying the ordinary sediment equation and the newly introduced sediment equation. Results of both numerical simulations were compared against laboratory measured data and also in case 1 with result of \textit{N. R. B. Olsen} and \textit{M. C. Melaaen} [``Three-dimensional calculation of scour around cylinders'', J. Hydraul. Eng. 119, No. 9, 1048--1054 (1993; \url{doi:10.1061/(ASCE)0733-9429(1993)119:9(1048) })]. Comparisons show that the new sediment formula could predict the scour more accurately than the ordinary one.Numerical solution of axi-symmetric jet mixing of incompressible dusty fluid considering Brownian diffusion and volume fraction.https://www.zbmath.org/1456.761332021-04-16T16:22:00+00:00"Dash, D. K."https://www.zbmath.org/authors/?q=ai:dash.d-k"Mishra, S. K."https://www.zbmath.org/authors/?q=ai:mishra.sabin-kumar|mishra.surya-kant|mishra.satyendra-kumar|mishra.sanjeev-kumar|mishra.shailendra-kumar|mishra.saroj-kumar|mishra.shashi-kant|mishra.saroj-kanta|mishra.shambhu-kumar|mishra.sudib-kumar|mishra.surendra-kumar|mishra.sudhir-k"Dash, Arun"https://www.zbmath.org/authors/?q=ai:dash.arunSummary: The effect of Brownian diffusion as well as finite volume fraction of suspended particulate matter on axially symmetrical jet mixing of incompressible dusty fluid has been studied. Assuming the velocity and temperature in the jet to differ only slightly from that of the surrounding stream, a perturbation method has been employed to linearize the basic equations. The linearized boundary layer equations have been solved by using Hankel transform technique and Crank- Nicolson finite difference technique. Numerical computations have been made to discuss the profiles of velocity and temperature of the fluid and particle. It is observed that the consideration of Brownian diffusion helps in migration of particles through a longer distance and decreases the magnitude of velocity of the particles considerably which helps in the settling of suspended particulate matter.Inelastic Maxwell models for monodisperse gas--solid flows.https://www.zbmath.org/1456.828212021-04-16T16:22:00+00:00"Kubicki, Aleksander"https://www.zbmath.org/authors/?q=ai:kubicki.aleksander"Garzó, Vicente"https://www.zbmath.org/authors/?q=ai:garzo.vicenteCoupling of a two phase gas liquid compositional 3D Darcy flow with a 1D compositional free gas flow.https://www.zbmath.org/1456.650822021-04-16T16:22:00+00:00"Brenner, K."https://www.zbmath.org/authors/?q=ai:brenner.konstantin"Masson, R."https://www.zbmath.org/authors/?q=ai:masson.roland"Trenty, L."https://www.zbmath.org/authors/?q=ai:trenty.laurent"Zhang, Y."https://www.zbmath.org/authors/?q=ai:zhang.yumengSummary: A model coupling a three dimensional gas liquid compositional Darcy flow and a one dimensional compositional free gas flow is presented. The coupling conditions at the interface between the gallery and the porous medium account for the molar normal fluxes continuity for each component, the gas liquid thermodynamical equilibrium, the gas pressure continuity and the gas and liquid molar fractions continuity. This model is applied to the simulation of the mass exchanges at the interface between the repository and the ventilation excavated gallery in a nuclear waste geological repository. The spatial discretization is essentially nodal and based on the vertex approximate gradient (VAG) scheme. Compared with classical nodal approaches such as the Control Volume Finite Element method, the VAG scheme has the advantage to avoid the mixture of different material properties and models in the control volumes located at the interfaces. The discrete model is validated using a quasi analytical solution for the stationary state, and the convergence of the VAG discretization is analysed for a simplified model coupling the Richards approximation in the porous medium and the gas pressure equation in the gallery.DuMu\(^{\text x} 3\) -- an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling.https://www.zbmath.org/1456.760792021-04-16T16:22:00+00:00"Koch, Timo"https://www.zbmath.org/authors/?q=ai:koch.timo"Gläser, Dennis"https://www.zbmath.org/authors/?q=ai:glaser.dennis"Weishaupt, Kilian"https://www.zbmath.org/authors/?q=ai:weishaupt.kilian"Ackermann, Sina"https://www.zbmath.org/authors/?q=ai:ackermann.sina"Beck, Martin"https://www.zbmath.org/authors/?q=ai:beck.martin"Becker, Beatrix"https://www.zbmath.org/authors/?q=ai:becker.beatrix"Burbulla, Samuel"https://www.zbmath.org/authors/?q=ai:burbulla.samuel"Class, Holger"https://www.zbmath.org/authors/?q=ai:class.holger"Coltman, Edward"https://www.zbmath.org/authors/?q=ai:coltman.edward"Emmert, Simon"https://www.zbmath.org/authors/?q=ai:emmert.simon"Fetzer, Thomas"https://www.zbmath.org/authors/?q=ai:fetzer.thomas"Grüninger, Christoph"https://www.zbmath.org/authors/?q=ai:gruninger.christoph"Heck, Katharina"https://www.zbmath.org/authors/?q=ai:heck.katharina"Hommel, Johannes"https://www.zbmath.org/authors/?q=ai:hommel.johannes"Kurz, Theresa"https://www.zbmath.org/authors/?q=ai:kurz.theresa"Lipp, Melanie"https://www.zbmath.org/authors/?q=ai:lipp.melanie"Mohammadi, Farid"https://www.zbmath.org/authors/?q=ai:mohammadi.farid-ghareh"Scherrer, Samuel"https://www.zbmath.org/authors/?q=ai:scherrer.samuel"Schneider, Martin"https://www.zbmath.org/authors/?q=ai:schneider.martin.3"Seitz, Gabriele"https://www.zbmath.org/authors/?q=ai:seitz.gabriele"Stadler, Leopold"https://www.zbmath.org/authors/?q=ai:stadler.leopold"Utz, Martin"https://www.zbmath.org/authors/?q=ai:utz.martin"Weinhardt, Felix"https://www.zbmath.org/authors/?q=ai:weinhardt.felix"Flemisch, Bernd"https://www.zbmath.org/authors/?q=ai:flemisch.berndSummary: We present version 3 of the open-source simulator for flow and transport processes in porous media DuMu\(^{\text x}\). DuMu\(^{\text x}\) is based on the modular C++ framework \textsc{Dune} (Distributed and Unified Numerics Environment) and is developed as a research code with a focus on modularity and reusability. We describe recent efforts in improving the transparency and efficiency of the development process and community-building, as well as efforts towards quality assurance and reproducible research. In addition to a major redesign of many simulation components in order to facilitate setting up complex simulations in DuMu\(^{\text x}\), version 3 introduces a more consistent abstraction of finite volume schemes. Finally, the new framework for multi-domain simulations is described, and three numerical examples demonstrate its flexibility.On generalized diffusion and heat systems on an evolving surface with a boundary.https://www.zbmath.org/1456.351952021-04-16T16:22:00+00:00"Koba, Hajime"https://www.zbmath.org/authors/?q=ai:koba.hajimeThe author considers a bounded domain \(U\subset \mathbb{R}^{2}\) with a
piecewise Lipschitz continuous boundary and an evolving surface \(\Gamma
(t)\subset \mathbb{R}^{3}\), \(0 < t < T\leq +\infty \), defined through \(
\Gamma (t)=\{x=^{t}(x_{1},x_{2},x_{3})\in \mathbb{R}^{3};\) \(x=\widehat{x}
(X,t)\), \(X\in U\}\) with a piecewise Lipschitz continuous boundary. The
motion velocity \(w\) of the evolving surface \(\Gamma (t)\) is defined through \(
w(\widehat{x}(X,t),t)=\frac{\partial \widehat{x}}{\partial t}(X,t)\). The
first main purpose of the paper is to derive and study the generalized
diffusion system on the evolving surface \(\cup _{0 < t < T}\Gamma (t)\times \{t\}
\): \(\partial _{t}f+(w\cdot \nabla )f+(\mathrm{div}_{\Gamma })C=\mathrm{div}
_{\Gamma }\{e_{1}^{\prime }\left\vert \mathrm{grad}_{\Gamma }C\right\vert ^{2}
\mathrm{grad}_{\Gamma }C\}\). The proof is based on a surface divergence
theorem in this case: for every \(\varphi =^{t}(\varphi _{1},\varphi
_{2},\varphi _{3})\in C^{1}(\overline{\Gamma (t)})\), one has: \(\int_{\Gamma
(t)} \mathrm{div}_{\Gamma }\varphi d\mathcal{H}_{x}^{2}=-\int_{\Gamma (t)}
\mathrm{div}_{\Gamma }n(n\cdot \varphi )d\mathcal{H}_{x}^{2}+\int_{\partial \Gamma
(t)}\nu \cdot \varphi d\mathcal{H}_{x}^{1}\), where \(\nu \) is the unit outer
co-normal vector. The proof also uses a formula for the variation of a
dissipation energy: if \(e_{D}\) is a \(C^{1}\)-function, \(0 < t < T\), \(f\in
C^{2}(\Gamma (t))\), \(-1<\varepsilon <1\), \(\psi \in C_{0}^{1}(\Gamma (t))\),
and \(E_{D}[f+\varepsilon \psi ](t)=-\int_{\Gamma (t)}\frac{1}{2}
e_{D}(\left\vert \nabla _{\Gamma }(f+\varepsilon \psi )\right\vert ^{2})d
\mathcal{H}_{x}^{2}\), then \(\frac{d}{d\varepsilon }\mid _{\varepsilon
=0}E_{D}[f+\varepsilon \psi ]=\int_{\Gamma (t)} \mathrm{div}_{\Gamma
}\{e_{D}^{\prime }(\left\vert \mathrm{grad}_{\Gamma }f\right\vert ^{2})
\mathrm{grad}_{\Gamma }f\}\psi d\mathcal{H}_{x}^{2}\). Then the author proves that if
\(\frac{\partial C}{\partial \nu }\mid _{\Gamma (t)}=0\), any solution to the
diffusion system satisfies the conservation law \(\int_{\Gamma
(t_{2})}C(x,t_{2})d\mathcal{H}_{x}^{2}=\int_{\Gamma (t_{1})}C(x,t_{1})d
\mathcal{H}_{x}^{2}\) and the energy law \(\int_{\Gamma (t_{2})}\frac{1}{2}
\left\vert C(x,t_{2})\right\vert ^{2}d\mathcal{H}_{x}^{2}+
\int_{t_{1}}^{t_{2}}\int_{\Gamma (\tau )}e_{1}^{\prime }(\left\vert
\mathrm{grad}_{\Gamma }C\right\vert ^{2})\left\vert \mathrm{grad}_{\Gamma
}C\right\vert ^{2}d\mathcal{H}_{x}^{2}d\tau =\int_{\Gamma (t_{1})}\frac{1}{2}
\left\vert C(x,t_{1})\right\vert ^{2}d\mathcal{H}_{x}^{2}\) (\(t_{1}<t_{1}\)).
The author also derives and studies the generalized heat system on the
evolving surface \(\cup _{0<t<T}\Gamma (t)\times \{t\}\): \(\partial _{t}\rho
+(w\cdot \nabla )\rho +(\mathrm{div}_{\Gamma }w)\rho =0\), \(\rho \partial
_{t}\theta +\rho (w\cdot \nabla )\theta =e_{2}^{\prime }(\left\vert
\mathrm{grad}_{\Gamma }\theta \right\vert ^{2})\mathrm{grad}_{\Gamma }\theta \). For
the proof, the author first derives a transport equation for every \(f\in
C^{1}(\Gamma (t))\) and \(\Omega (t)\subset \Gamma (t)\), \(\frac{d}{
d\varepsilon }\int_{\Omega (t)}f(x,t)d\mathcal{H}_{x}^{2}=\int_{\Omega
(t)}\{\partial _{t}f+(w\cdot \nabla )f+(\mathrm{div}_{\Gamma }w)\rho \}(x,t)d
\mathcal{H}_{x}^{2}\). In the two last parts of his paper, the author
considers the case of an evolving double bubble. He here proves divergence
and transport theorems and he proposes a mathematical model for a diffusion
process on an evolving double bubble from an energetic point of view.
Reviewer: Alain Brillard (Riedisheim)Effect of volume fraction along with concentration parameter in the dusty incompressible fluid.https://www.zbmath.org/1456.761352021-04-16T16:22:00+00:00"Rath, B. K."https://www.zbmath.org/authors/?q=ai:rath.b-k"Mahapatro, P. K."https://www.zbmath.org/authors/?q=ai:mahapatro.p-k"Dash, D. K."https://www.zbmath.org/authors/?q=ai:dash.d-kSummary: The effect of finite volume fraction of suspended particulate matter on axially symmetrical jet mixing of incompressible dusty fluid has been considered. Assuming the velocity and temperature in the jet to differ slightly from the surrounding stream, a perturbation method has been employed to linearize the nonlinear differential equation. The linear equations have been solved by using Laplace transformation technique. Numerical computations have been made to discuss the magnitude of the longitudinal perturbated fluid velocity. It is observed that increase in concentration parameter of dust particle reduces the magnitude of fluid velocity significantly.Dynamics and stability of sessile drops with contact points.https://www.zbmath.org/1456.351542021-04-16T16:22:00+00:00"Tice, Ian"https://www.zbmath.org/authors/?q=ai:tice.ian"Wu, Lei"https://www.zbmath.org/authors/?q=ai:wu.lei.1Authors' abstract: The authors consider the dynamics of a two-dimensional droplet of incompressible viscous fluid evolving above a one-dimensional flat surface under the influence of gravity. This is a free boundary problem: the interface between the fluid on the surface and the air above is free to move and experience capillary forces. A mathematical model of this problem is formulated and some a priori estimates are obtained. These estimates are used to show that for initial data sufficiently close to equilibrium, there exist global solutions of the model that decay to a shifted equilibrium exponentially fast.
Reviewer: Gheorghe Moroşanu (Cluj-Napoca)