Chugainova, A. P.; Polekhina, R. R. Nonuniqueness of a self-similar solution to the Riemann problem for elastic waves in media with a negative nonlinearity parameter. (English. Russian original) Zbl 07781677 Proc. Steklov Inst. Math. 322, 242-256 (2023); translation from Tr. Mat. Inst. Steklova 322, 251-265 (2023). MSC: 35A02 35C06 35L45 35L60 35L67 PDFBibTeX XMLCite \textit{A. P. Chugainova} and \textit{R. R. Polekhina}, Proc. Steklov Inst. Math. 322, 242--256 (2023; Zbl 07781677); translation from Tr. Mat. Inst. Steklova 322, 251--265 (2023) Full Text: DOI
Wang, Zhenming; Zhu, Jun; Tian, Linlin; Zhao, Ning Hybrid fifth-order unequal-sized weighted essentially non-oscillatory scheme for shallow water equations. (English) Zbl 07772631 Comput. Math. Appl. 150, 1-14 (2023). MSC: 76B15 65M06 76M20 76M12 35L65 PDFBibTeX XMLCite \textit{Z. Wang} et al., Comput. Math. Appl. 150, 1--14 (2023; Zbl 07772631) Full Text: DOI
Yu, Changsheng; Liu, T. G.; Feng, Chengliang A well-balanced scheme for Euler equations with singular sources. (English) Zbl 07735429 SIAM J. Sci. Comput. 45, No. 4, A2119-A2151 (2023). MSC: 65-XX 35L86 35Q31 65M60 76N30 PDFBibTeX XMLCite \textit{C. Yu} et al., SIAM J. Sci. Comput. 45, No. 4, A2119--A2151 (2023; Zbl 07735429) Full Text: DOI arXiv
Kovyrkina, O. A.; Ostapenko, V. V. On accuracy of finite-difference schemes in calculations of centered rarefaction waves. (Russian. English summary) Zbl 07720896 Mat. Model. 35, No. 7, 83-96 (2023). MSC: 65Mxx 76-XX PDFBibTeX XMLCite \textit{O. A. Kovyrkina} and \textit{V. V. Ostapenko}, Mat. Model. 35, No. 7, 83--96 (2023; Zbl 07720896) Full Text: DOI MNR
Neelan, A. Arun Govind; Chandran, R. Jishnu; Diaz, Manuel A.; Bürger, Raimund An efficient three-level weighted essentially non-oscillatory scheme for hyperbolic equations. (English) Zbl 1509.65084 Comput. Appl. Math. 42, No. 2, Paper No. 70, 23 p. (2023). MSC: 65M08 65M06 65N08 65L06 65M12 35F61 35L50 76N15 76J20 76L05 76Q05 35Q31 PDFBibTeX XMLCite \textit{A. A. G. Neelan} et al., Comput. Appl. Math. 42, No. 2, Paper No. 70, 23 p. (2023; Zbl 1509.65084) Full Text: DOI
Favrie, N.; Lombard, B. A hyperbolic generalized Zener model for nonlinear viscoelastic waves. (English) Zbl 1524.74281 Wave Motion 116, Article ID 103086, 18 p. (2023). MSC: 74J30 86A15 74B20 74D10 PDFBibTeX XMLCite \textit{N. Favrie} and \textit{B. Lombard}, Wave Motion 116, Article ID 103086, 18 p. (2023; Zbl 1524.74281) Full Text: DOI
Zhang, Qinglong; Liu, Shuzhi The Riemann problem and a Godunov-type scheme for a traffic flow model on two lanes with two velocities. (English) Zbl 1510.35183 Appl. Math. Comput. 436, Article ID 127502, 15 p. (2023). MSC: 35L65 35L50 35L60 35Q35 PDFBibTeX XMLCite \textit{Q. Zhang} and \textit{S. Liu}, Appl. Math. Comput. 436, Article ID 127502, 15 p. (2023; Zbl 1510.35183) Full Text: DOI
Briani, M.; Puppo, G.; Ribot, M. Angle dependence in coupling conditions for shallow water equations at channel junctions. (English) Zbl 1524.35380 Comput. Math. Appl. 108, 49-65 (2022). MSC: 35L65 76B15 35Q35 76M12 65M60 PDFBibTeX XMLCite \textit{M. Briani} et al., Comput. Math. Appl. 108, 49--65 (2022; Zbl 1524.35380) Full Text: DOI arXiv
Aregba-Driollet, Denise; Brull, Stéphane; Prigent, Corentin A discrete velocity numerical scheme for the two-dimensional bitemperature Euler system. (English) Zbl 1482.65158 SIAM J. Numer. Anal. 60, No. 1, 28-51 (2022). Reviewer: Victor Michel-Dansac (Strasbourg) MSC: 65M08 65M06 65N08 35L60 76X05 76L05 35Q31 82C40 82D75 PDFBibTeX XMLCite \textit{D. Aregba-Driollet} et al., SIAM J. Numer. Anal. 60, No. 1, 28--51 (2022; Zbl 1482.65158) Full Text: DOI
Israwi, Samer; Kalisch, Henrik; Katsaounis, Theodoros; Mitsotakis, Dimitrios A regularized shallow-water waves system with slip-wall boundary conditions in a basin: theory and numerical analysis. (English) Zbl 1481.35331 Nonlinearity 35, No. 1, 750-786 (2022). MSC: 35Q35 76B15 35C08 35B65 35B45 35B40 65M60 65L06 65N30 65M12 65M15 PDFBibTeX XMLCite \textit{S. Israwi} et al., Nonlinearity 35, No. 1, 750--786 (2022; Zbl 1481.35331) Full Text: DOI arXiv
Biswas, Tirtha Roy; Dey, Subhasish; Sen, Dhrubajyoti Modeling positive surge propagation in open channels using the Serre-Green-Naghdi equations. (English) Zbl 1481.76042 Appl. Math. Modelling 97, 803-820 (2021). MSC: 76B15 76M12 PDFBibTeX XMLCite \textit{T. R. Biswas} et al., Appl. Math. Modelling 97, 803--820 (2021; Zbl 1481.76042) Full Text: DOI
Michel-Dansac, Victor; Berthon, Christophe; Clain, Stéphane; Foucher, Françoise A two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning friction. (English) Zbl 1521.76454 Comput. Fluids 230, Article ID 105152, 21 p. (2021). MSC: 76M12 65M08 65M12 76B15 PDFBibTeX XMLCite \textit{V. Michel-Dansac} et al., Comput. Fluids 230, Article ID 105152, 21 p. (2021; Zbl 1521.76454) Full Text: DOI arXiv HAL
Sheng, Wancheng; Zhang, Qinglong; Zheng, Yuxi A direct Eulerian GRP scheme for a blood flow model in arteries. (English) Zbl 1486.92004 SIAM J. Sci. Comput. 43, No. 3, A1975-A1996 (2021). Reviewer: Zhiming Chen (Beijing) MSC: 92-08 65M06 65M25 76M20 35L60 35L65 35L67 35R03 76L05 76N10 76Z05 92C35 35Q92 PDFBibTeX XMLCite \textit{W. Sheng} et al., SIAM J. Sci. Comput. 43, No. 3, A1975--A1996 (2021; Zbl 1486.92004) Full Text: DOI arXiv
Beisiegel, Nicole; Castro, Cristóbal E.; Behrens, Jörn Metrics for performance quantification of adaptive mesh refinement. (English) Zbl 1471.65133 J. Sci. Comput. 87, No. 1, Paper No. 36, 24 p. (2021). Reviewer: Yinhua Xia (Hefei) MSC: 65M60 65N50 76B15 76B47 86A05 86A10 35Q35 PDFBibTeX XMLCite \textit{N. Beisiegel} et al., J. Sci. Comput. 87, No. 1, Paper No. 36, 24 p. (2021; Zbl 1471.65133) Full Text: DOI
Berthon, Christophe; M’baye, Meissa; Le, Minh; Seck, Diaraf A well-defined moving steady states capturing Godunov-type scheme for shallow-water model. (English) Zbl 1490.76142 Int. J. Finite Vol. 15, Article ID hal-031929541, 33 p. (2020). MSC: 76M12 65M08 35L65 76B15 PDFBibTeX XMLCite \textit{C. Berthon} et al., Int. J. Finite Vol. 15, Article ID hal-031929541, 33 p. (2020; Zbl 1490.76142) Full Text: HAL
Biswas, Biswarup; Dubey, Ritesh Kumar ENO and WENO schemes using arc-length based smoothness measurement. (English) Zbl 1524.65317 Comput. Math. Appl. 80, No. 12, 2780-2795 (2020). MSC: 65M06 35L65 65M12 76M20 76L05 35B05 35B38 35L67 PDFBibTeX XMLCite \textit{B. Biswas} and \textit{R. K. Dubey}, Comput. Math. Appl. 80, No. 12, 2780--2795 (2020; Zbl 1524.65317) Full Text: DOI arXiv
Wang, Zhenming; Zhu, Jun; Zhao, Ning A new fifth-order finite difference well-balanced multi-resolution WENO scheme for solving shallow water equations. (English) Zbl 1447.65033 Comput. Math. Appl. 80, No. 5, 1387-1404 (2020). MSC: 65M06 65M08 65M12 76M20 76M12 76B15 76L05 35Q35 PDFBibTeX XMLCite \textit{Z. Wang} et al., Comput. Math. Appl. 80, No. 5, 1387--1404 (2020; Zbl 1447.65033) Full Text: DOI
Goudiaby, Mouhamadou Samsidy; Kreiss, Gunilla Existence result for the coupling of shallow water and Borda-Carnot equations with Riemann data. (English) Zbl 1447.35266 J. Hyperbolic Differ. Equ. 17, No. 1, 185-212 (2020). MSC: 35Q35 76B15 15A18 35L50 35A01 35A02 PDFBibTeX XMLCite \textit{M. S. Goudiaby} and \textit{G. Kreiss}, J. Hyperbolic Differ. Equ. 17, No. 1, 185--212 (2020; Zbl 1447.35266) Full Text: DOI
Maranzoni, Andrea; Mignosa, Paolo Seismic-generated unsteady motions in shallow basins and channels. II: Numerical modelling. (English) Zbl 1481.86021 Appl. Math. Modelling 68, 712-731 (2019). MSC: 86A15 76B15 PDFBibTeX XMLCite \textit{A. Maranzoni} and \textit{P. Mignosa}, Appl. Math. Modelling 68, 712--731 (2019; Zbl 1481.86021) Full Text: DOI
Zijlema, Marcel The role of the Rankine-Hugoniot relations in staggered finite difference schemes for the shallow water equations. (English) Zbl 1519.76026 Comput. Fluids 192, Article ID 104274, 18 p. (2019). MSC: 76B15 76M20 PDFBibTeX XMLCite \textit{M. Zijlema}, Comput. Fluids 192, Article ID 104274, 18 p. (2019; Zbl 1519.76026) Full Text: DOI Link
Jagtap, Ameya D. Method of relaxed streamline upwinding for hyperbolic conservation laws. (English) Zbl 1469.65148 Wave Motion 78, 132-161 (2018). MSC: 65M60 35L65 65M15 76B15 PDFBibTeX XMLCite \textit{A. D. Jagtap}, Wave Motion 78, 132--161 (2018; Zbl 1469.65148) Full Text: DOI arXiv
Kesserwani, Georges; Ayog, Janice Lynn; Bau, Domenico Discontinuous Galerkin formulation for 2D hydrodynamic modelling: trade-offs between theoretical complexity and practical convenience. (English) Zbl 1440.76074 Comput. Methods Appl. Mech. Eng. 342, 710-741 (2018). MSC: 76M10 65M60 76B15 PDFBibTeX XMLCite \textit{G. Kesserwani} et al., Comput. Methods Appl. Mech. Eng. 342, 710--741 (2018; Zbl 1440.76074) Full Text: DOI
Samii, Ali; Dawson, Clint An explicit hybridized discontinuous Galerkin method for Serre-Green-Naghdi wave model. (English) Zbl 1439.76094 Comput. Methods Appl. Mech. Eng. 330, 447-470 (2018). MSC: 76M10 65M60 76B15 86A05 PDFBibTeX XMLCite \textit{A. Samii} and \textit{C. Dawson}, Comput. Methods Appl. Mech. Eng. 330, 447--470 (2018; Zbl 1439.76094) Full Text: DOI
Kurganov, Alexander Finite-volume schemes for shallow-water equations. (English) Zbl 1430.76372 Acta Numerica 27, 289-351 (2018). MSC: 76M12 65M08 35L65 76B15 76-02 PDFBibTeX XMLCite \textit{A. Kurganov}, Acta Numerica 27, 289--351 (2018; Zbl 1430.76372) Full Text: DOI
Navas-Montilla, A.; Murillo, J. 2D well-balanced augmented ADER schemes for the shallow water equations with bed elevation and extension to the rotating frame. (English) Zbl 1415.76476 J. Comput. Phys. 372, 316-348 (2018). MSC: 76M12 76B15 35L50 35Q35 PDFBibTeX XMLCite \textit{A. Navas-Montilla} and \textit{J. Murillo}, J. Comput. Phys. 372, 316--348 (2018; Zbl 1415.76476) Full Text: DOI Link
Chiapolino, Alexandre; Saurel, Richard Models and methods for two-layer shallow water flows. (English) Zbl 1415.76061 J. Comput. Phys. 371, 1043-1066 (2018). MSC: 76B15 76D27 76M12 76T99 PDFBibTeX XMLCite \textit{A. Chiapolino} and \textit{R. Saurel}, J. Comput. Phys. 371, 1043--1066 (2018; Zbl 1415.76061) Full Text: DOI Link
Berthon, Christophe; Michel-Dansac, Victor A simple fully well-balanced and entropy preserving scheme for the shallow-water equations. (English) Zbl 1410.65338 Appl. Math. Lett. 86, 284-290 (2018). MSC: 65M08 65M12 35Q35 76B15 PDFBibTeX XMLCite \textit{C. Berthon} and \textit{V. Michel-Dansac}, Appl. Math. Lett. 86, 284--290 (2018; Zbl 1410.65338) Full Text: DOI HAL
Gavrilyuk, S.; Ivanova, K.; Favrie, N. Multi-dimensional shear shallow water flows: problems and solutions. (English) Zbl 1406.65068 J. Comput. Phys. 366, 252-280 (2018). MSC: 65M08 35Q35 35L45 76B15 35L67 PDFBibTeX XMLCite \textit{S. Gavrilyuk} et al., J. Comput. Phys. 366, 252--280 (2018; Zbl 1406.65068) Full Text: DOI HAL
Abdelrahman, Mahmoud A. E. Numerical investigation of the wave-front tracking algorithm for the full ultra-relativistic Euler equations. (English) Zbl 1401.35212 Int. J. Nonlinear Sci. Numer. Simul. 19, No. 2, 223-229 (2018). MSC: 35L65 35L45 35L60 35L67 35Q31 35Q75 76Y05 PDFBibTeX XMLCite \textit{M. A. E. Abdelrahman}, Int. J. Nonlinear Sci. Numer. Simul. 19, No. 2, 223--229 (2018; Zbl 1401.35212) Full Text: DOI
Hosseinzadeh-Tabrizi, Alireza; Ghaeini-Hessaroeyeh, Mahnaz Modelling of dam failure-induced flows over movable beds considering turbulence effects. (English) Zbl 1390.76443 Comput. Fluids 161, 199-210 (2018). MSC: 76M12 65M08 76B15 PDFBibTeX XMLCite \textit{A. Hosseinzadeh-Tabrizi} and \textit{M. Ghaeini-Hessaroeyeh}, Comput. Fluids 161, 199--210 (2018; Zbl 1390.76443) Full Text: DOI
Chertock, Alina; Dudzinski, Michael; Kurganov, Alexander; Lukáčová-Medvid’ová, Mária Well-balanced schemes for the shallow water equations with Coriolis forces. (English) Zbl 1448.65097 Numer. Math. 138, No. 4, 939-973 (2018). MSC: 65M06 65N08 35L45 35L65 65M25 65M15 76B15 76U60 76U65 35Q86 86A05 65J10 PDFBibTeX XMLCite \textit{A. Chertock} et al., Numer. Math. 138, No. 4, 939--973 (2018; Zbl 1448.65097) Full Text: DOI
Maeda, Kazuki; Colonius, Tim A source term approach for generation of one-way acoustic waves in the Euler and Navier-Stokes equations. (English) Zbl 1524.76394 Wave Motion 75, 36-49 (2017). MSC: 76Q05 76B15 76D33 76M20 65M06 PDFBibTeX XMLCite \textit{K. Maeda} and \textit{T. Colonius}, Wave Motion 75, 36--49 (2017; Zbl 1524.76394) Full Text: DOI
Mercier, Jean-François; Lombard, Bruno A two-way model for nonlinear acoustic waves in a non-uniform lattice of Helmholtz resonators. (English) Zbl 1524.35547 Wave Motion 72, 260-275 (2017). MSC: 35Q53 35C08 35Q35 76Q05 PDFBibTeX XMLCite \textit{J.-F. Mercier} and \textit{B. Lombard}, Wave Motion 72, 260--275 (2017; Zbl 1524.35547) Full Text: DOI arXiv
Ivanova, K. A.; Gavrilyuk, S. L.; Nkonga, B.; Richard, G. L. Formation and coarsening of roll-waves in shear shallow water flows down an inclined rectangular channel. (English) Zbl 1390.76042 Comput. Fluids 159, 189-203 (2017). MSC: 76B15 76M12 65M08 PDFBibTeX XMLCite \textit{K. A. Ivanova} et al., Comput. Fluids 159, 189--203 (2017; Zbl 1390.76042) Full Text: DOI HAL
Bourdarias, Christian; Gerbi, Stéphane; Lteif, Ralph A numerical scheme for an improved Green-Naghdi model in the Camassa-Holm regime for the propagation of internal waves. (English) Zbl 1390.76400 Comput. Fluids 156, 283-304 (2017). MSC: 76M12 65M08 76B55 76M20 65M06 PDFBibTeX XMLCite \textit{C. Bourdarias} et al., Comput. Fluids 156, 283--304 (2017; Zbl 1390.76400) Full Text: DOI arXiv
Kim, Mi-Young; Park, Eun-Jae; Shin, Jaemin High-order discontinuous Galerkin methods with Lagrange multiplier for hyperbolic systems of conservation laws. (English) Zbl 1373.65070 Comput. Math. Appl. 73, No. 9, 1945-1974 (2017). MSC: 65M60 35L65 35L50 35Q53 76B15 76M10 65M12 76N15 PDFBibTeX XMLCite \textit{M.-Y. Kim} et al., Comput. Math. Appl. 73, No. 9, 1945--1974 (2017; Zbl 1373.65070) Full Text: DOI
Chandrashekar, Praveen; Zenk, Markus Well-balanced nodal discontinuous Galerkin method for Euler equations with gravity. (English) Zbl 1462.65180 J. Sci. Comput. 71, No. 3, 1062-1093 (2017). MSC: 65N30 65D32 76B15 76N06 76M10 35Q31 PDFBibTeX XMLCite \textit{P. Chandrashekar} and \textit{M. Zenk}, J. Sci. Comput. 71, No. 3, 1062--1093 (2017; Zbl 1462.65180) Full Text: DOI arXiv
Käppeli, Roger A well-balanced scheme for the Euler equations with gravitation. (English) Zbl 1371.35206 Gosse, Laurent (ed.) et al., Innovative algorithms and analysis. Based on the presentations at the workshop, Rome, Italy, May 17–20, 2016. Cham: Springer (ISBN 978-3-319-49261-2/hbk; 978-3-319-49262-9/ebook). Springer INdAM Series 16, 229-241 (2017). MSC: 35Q31 76B15 85A05 86A10 76M12 65M08 PDFBibTeX XMLCite \textit{R. Käppeli}, Springer INdAM Ser. 16, 229--241 (2017; Zbl 1371.35206) Full Text: DOI
Michel-Dansac, Victor; Berthon, Christophe; Clain, Stéphane; Foucher, Françoise A well-balanced scheme for the shallow-water equations with topography. (English) Zbl 1359.76206 Comput. Math. Appl. 72, No. 3, 568-593 (2016). MSC: 76M20 65M06 65M25 76B15 PDFBibTeX XMLCite \textit{V. Michel-Dansac} et al., Comput. Math. Appl. 72, No. 3, 568--593 (2016; Zbl 1359.76206) Full Text: DOI
Bui-Thanh, Tan Construction and analysis of HDG methods for linearized shallow water equations. (English) Zbl 1457.65098 SIAM J. Sci. Comput. 38, No. 6, A3696-A3719 (2016). MSC: 65M60 65M12 65M15 65M22 76B15 76M10 86A05 35Q35 PDFBibTeX XMLCite \textit{T. Bui-Thanh}, SIAM J. Sci. Comput. 38, No. 6, A3696--A3719 (2016; Zbl 1457.65098) Full Text: DOI
Vanzo, Davide; Siviglia, Annunziato; Toro, Eleuterio F. Pollutant transport by shallow water equations on unstructured meshes: hyperbolization of the model and numerical solution via a novel flux splitting scheme. (English) Zbl 1349.76401 J. Comput. Phys. 321, 1-20 (2016). MSC: 76M12 65M08 65M12 76B15 PDFBibTeX XMLCite \textit{D. Vanzo} et al., J. Comput. Phys. 321, 1--20 (2016; Zbl 1349.76401) Full Text: DOI
Richoux, Olivier; Lombard, Bruno; Mercier, Jean-François Generation of acoustic solitary waves in a lattice of Helmholtz resonators. (English) Zbl 1454.76085 Wave Motion 56, 85-99 (2015). MSC: 76Q05 35F61 35C08 PDFBibTeX XMLCite \textit{O. Richoux} et al., Wave Motion 56, 85--99 (2015; Zbl 1454.76085) Full Text: DOI HAL
Katta, Kiran K.; Nair, Ramachandran D.; Kumar, Vinod High-order finite volume shallow water model on the cubed-sphere: 1D reconstruction scheme. (English) Zbl 1410.76237 Appl. Math. Comput. 266, 316-327 (2015). MSC: 76M12 65M08 65M50 76B15 86A05 PDFBibTeX XMLCite \textit{K. K. Katta} et al., Appl. Math. Comput. 266, 316--327 (2015; Zbl 1410.76237) Full Text: DOI
Gerhard, Nils; Caviedes-Voullième, Daniel; Müller, Siegfried; Kesserwani, Georges Multiwavelet-based grid adaptation with discontinuous Galerkin schemes for shallow water equations. (English) Zbl 1349.76206 J. Comput. Phys. 301, 265-288 (2015). MSC: 76M10 65M60 65T60 76B15 PDFBibTeX XMLCite \textit{N. Gerhard} et al., J. Comput. Phys. 301, 265--288 (2015; Zbl 1349.76206) Full Text: DOI Link
Berthon, Christophe; Foucher, Françoise; Morales, Tomás An efficient splitting technique for two-layer shallow-water model. (English) Zbl 1338.76073 Numer. Methods Partial Differ. Equations 31, No. 5, 1396-1423 (2015). MSC: 76M12 65M08 76B15 PDFBibTeX XMLCite \textit{C. Berthon} et al., Numer. Methods Partial Differ. Equations 31, No. 5, 1396--1423 (2015; Zbl 1338.76073) Full Text: DOI
Murillo, J.; García-Navarro, P. Accurate numerical modeling of 1D flow in channels with arbitrary shape. Application of the energy balanced property. (English) Zbl 1349.76032 J. Comput. Phys. 260, 222-248 (2014). MSC: 76B15 76M20 65M06 PDFBibTeX XMLCite \textit{J. Murillo} and \textit{P. García-Navarro}, J. Comput. Phys. 260, 222--248 (2014; Zbl 1349.76032) Full Text: DOI
Pudjaprasetya, S. R.; Magdalena, I. Momentum conservative schemes for shallow water flows. (English) Zbl 1309.76138 East Asian J. Appl. Math. 4, No. 2, 152-165 (2014). MSC: 76M12 65M08 76B15 35L65 PDFBibTeX XMLCite \textit{S. R. Pudjaprasetya} and \textit{I. Magdalena}, East Asian J. Appl. Math. 4, No. 2, 152--165 (2014; Zbl 1309.76138) Full Text: DOI Link
Chertock, Alina; Kurganov, Alexander; Liu, Yu Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients. (English) Zbl 1342.76081 Numer. Math. 127, No. 4, 595-639 (2014). MSC: 76M12 76B15 65M08 86A05 35L65 35L67 PDFBibTeX XMLCite \textit{A. Chertock} et al., Numer. Math. 127, No. 4, 595--639 (2014; Zbl 1342.76081) Full Text: DOI
Karelsky, Kirill V.; Petrosyan, Arakel S.; Slavin, Alexander G. Quasi-two-layer finite-volume scheme for modelling shallow water flows over an arbitrary bed in the presence of external force. II: Algorithm applications and numerical results. (English) Zbl 1291.65268 Russ. J. Numer. Anal. Math. Model. 29, No. 3, 179-195 (2014). MSC: 65M08 76B07 76B15 35Q35 74S10 76S05 PDFBibTeX XMLCite \textit{K. V. Karelsky} et al., Russ. J. Numer. Anal. Math. Model. 29, No. 3, 179--195 (2014; Zbl 1291.65268) Full Text: DOI
Karelsky, Kirill V.; Petrosyan, Arakel S.; Slavin, Aleksander G. Quasi-two-layer finite-volume scheme for modelling shallow water flows over an arbitrary bed in the presence of external force. I: Algorithm development and validation. (English) Zbl 1357.76048 Russ. J. Numer. Anal. Math. Model. 29, No. 1, 25-46 (2014). MSC: 76M12 76B07 76B15 65M08 65M06 PDFBibTeX XMLCite \textit{K. V. Karelsky} et al., Russ. J. Numer. Anal. Math. Model. 29, No. 1, 25--46 (2014; Zbl 1357.76048) Full Text: DOI
Hou, Jingming; Liang, Qiuhua; Simons, Franz; Hinkelmann, Reinhard A stable 2D unstructured shallow flow model for simulations of wetting and drying over rough terrains. (English) Zbl 1290.76083 Comput. Fluids 82, 132-147 (2013). MSC: 76M12 76B15 PDFBibTeX XMLCite \textit{J. Hou} et al., Comput. Fluids 82, 132--147 (2013; Zbl 1290.76083) Full Text: DOI
Hou, Jingming; Simons, Franz; Mahgoub, Mohamed; Hinkelmann, Reinhard A robust well-balanced model on unstructured grids for shallow water flows with wetting and drying over complex topography. (English) Zbl 1286.76020 Comput. Methods Appl. Mech. Eng. 257, 126-149 (2013). MSC: 76B15 76M12 PDFBibTeX XMLCite \textit{J. Hou} et al., Comput. Methods Appl. Mech. Eng. 257, 126--149 (2013; Zbl 1286.76020) Full Text: DOI
Murillo, J.; García-Navarro, P. Augmented versions of the HLL and HLLC Riemann solvers including source terms in one and two dimensions for shallow flow applications. (English) Zbl 1284.35118 J. Comput. Phys. 231, No. 20, 6861-6906 (2012). MSC: 35D30 35Q35 65M08 76M12 76B15 PDFBibTeX XMLCite \textit{J. Murillo} and \textit{P. García-Navarro}, J. Comput. Phys. 231, No. 20, 6861--6906 (2012; Zbl 1284.35118) Full Text: DOI
Dodd, Nicholas; Machardy, Laura C. A 1D Roe decomposition of a system of equations governing wave height transformation. (English) Zbl 1253.76008 Int. J. Numer. Methods Fluids 69, No. 7, 1271-1282 (2012). MSC: 76B15 76M12 65M08 PDFBibTeX XMLCite \textit{N. Dodd} and \textit{L. C. Machardy}, Int. J. Numer. Methods Fluids 69, No. 7, 1271--1282 (2012; Zbl 1253.76008) Full Text: DOI
Castro Díaz, M. J.; Fernández-Nieto, E. A class of computationally fast first order finite volume solvers: PVM methods. (English) Zbl 1253.65167 SIAM J. Sci. Comput. 34, No. 4, A2173-A2196 (2012). MSC: 65N06 76B15 76M20 76N99 PDFBibTeX XMLCite \textit{M. J. Castro Díaz} and \textit{E. Fernández-Nieto}, SIAM J. Sci. Comput. 34, No. 4, A2173--A2196 (2012; Zbl 1253.65167) Full Text: DOI Link
Berthon, Christophe; Foucher, Françoise Efficient well-balanced hydrostatic upwind schemes for shallow-water equations. (English) Zbl 1351.76095 J. Comput. Phys. 231, No. 15, 4993-5015 (2012). MSC: 76M12 76B15 65M06 PDFBibTeX XMLCite \textit{C. Berthon} and \textit{F. Foucher}, J. Comput. Phys. 231, No. 15, 4993--5015 (2012; Zbl 1351.76095) Full Text: DOI
Chen, Y. G.; Price, W. G.; Temarel, P. An anti-diffusive volume of fluid method for interfacial fluid flows. (English) Zbl 1426.76348 Int. J. Numer. Methods Fluids 68, No. 3, 341-359 (2012). MSC: 76M12 76M20 76B15 76B10 PDFBibTeX XMLCite \textit{Y. G. Chen} et al., Int. J. Numer. Methods Fluids 68, No. 3, 341--359 (2012; Zbl 1426.76348) Full Text: DOI
Kesserwani, Georges; Liang, Qiuhua A conservative high-order discontinuous Galerkin method for the shallow water equations with arbitrary topography. (English) Zbl 1235.76067 Int. J. Numer. Methods Eng. 86, No. 1, 47-69 (2011). MSC: 76M10 76B15 PDFBibTeX XMLCite \textit{G. Kesserwani} and \textit{Q. Liang}, Int. J. Numer. Methods Eng. 86, No. 1, 47--69 (2011; Zbl 1235.76067) Full Text: DOI
Soares-Frazão, Sandra; Zech, Yves HLLC scheme with novel wave-speed estimators appropriate for two-dimensional shallow-water flow on erodible bed. (English) Zbl 1285.76025 Int. J. Numer. Methods Fluids 66, No. 8, 1019-1036 (2011). MSC: 76M12 76B15 65M08 PDFBibTeX XMLCite \textit{S. Soares-Frazão} and \textit{Y. Zech}, Int. J. Numer. Methods Fluids 66, No. 8, 1019--1036 (2011; Zbl 1285.76025) Full Text: DOI
Coulouvrat, François A quasi-analytical shock solution for general nonlinear progressive waves. (English) Zbl 1231.35163 Wave Motion 46, No. 2, 97-107 (2009). MSC: 35Q35 74J30 35L67 35L70 PDFBibTeX XMLCite \textit{F. Coulouvrat}, Wave Motion 46, No. 2, 97--107 (2009; Zbl 1231.35163) Full Text: DOI
Jaisankar, S.; Rao, S. V. Raghurama A central Rankine-Hugoniot solver for hyperbolic conservation laws. (English) Zbl 1158.65058 J. Comput. Phys. 228, No. 3, 770-798 (2009). MSC: 65M06 35L65 76M20 35Q53 76N15 76B15 76W05 PDFBibTeX XMLCite \textit{S. Jaisankar} and \textit{S. V. R. Rao}, J. Comput. Phys. 228, No. 3, 770--798 (2009; Zbl 1158.65058) Full Text: DOI
Bernard, P.-E.; Remacle, J.-F.; Legat, V. Boundary discretization for high-order discontinuous Galerkin computations of tidal flows around shallow water islands. (English) Zbl 1394.76076 Int. J. Numer. Methods Fluids 59, No. 5, 535-557 (2009). MSC: 76M15 65M60 76B15 86A05 86A10 PDFBibTeX XMLCite \textit{P. E. Bernard} et al., Int. J. Numer. Methods Fluids 59, No. 5, 535--557 (2009; Zbl 1394.76076) Full Text: DOI
Rhebergen, S.; Bokhove, O.; van der Vegt, J. J. W. Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations. (English) Zbl 1153.65097 J. Comput. Phys. 227, No. 3, 1887-1922 (2008). Reviewer: Roland Pulch (Wuppertal) MSC: 65M60 35L60 35L65 35L67 76M10 76B15 76T10 PDFBibTeX XMLCite \textit{S. Rhebergen} et al., J. Comput. Phys. 227, No. 3, 1887--1922 (2008; Zbl 1153.65097) Full Text: DOI Link
Skoula, Z. D.; Borthwick, A. G. L.; Moutzouris, C. I. Godunov-type solution of the shallow water equations on adaptive unstructured triangular grids. (English) Zbl 1184.76754 Int. J. Comput. Fluid Dyn. 20, No. 9, 621-636 (2006). MSC: 76M12 76B15 86A05 PDFBibTeX XMLCite \textit{Z. D. Skoula} et al., Int. J. Comput. Fluid Dyn. 20, No. 9, 621--636 (2006; Zbl 1184.76754) Full Text: DOI
Giraldo, Francis X. High-order triangle-based discontinuous Galerkin methods for hyperbolic equations on a rotating sphere. (English) Zbl 1089.65096 J. Comput. Phys. 214, No. 2, 447-465 (2006). MSC: 65M60 65M06 35L65 76B15 76M12 76M10 PDFBibTeX XMLCite \textit{F. X. Giraldo}, J. Comput. Phys. 214, No. 2, 447--465 (2006; Zbl 1089.65096) Full Text: DOI
Guinot, Vincent; Soares-Frazão, Sandra Flux and source term discretization in two-dimensional shallow water models with porosity on unstructured grids. (English) Zbl 1086.76048 Int. J. Numer. Methods Fluids 50, No. 3, 309-345 (2006). MSC: 76M12 76S05 76B15 86A05 PDFBibTeX XMLCite \textit{V. Guinot} and \textit{S. Soares-Frazão}, Int. J. Numer. Methods Fluids 50, No. 3, 309--345 (2006; Zbl 1086.76048) Full Text: DOI
Castro, M. J.; Ferreiro Ferreiro, A. M.; García-Rodríguez, J. A.; González-Vida, J. M.; Macías, J.; Parés, C.; Vázquez-Cendón, M. Elena The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems. (English) Zbl 1121.76008 Math. Comput. Modelling 42, No. 3-4, 419-439 (2005). MSC: 76B07 76B15 76B55 76M20 65M06 PDFBibTeX XMLCite \textit{M. J. Castro} et al., Math. Comput. Modelling 42, No. 3--4, 419--439 (2005; Zbl 1121.76008) Full Text: DOI
Parés, Carlos; Castro, Manuel On the well-balance property of Roe’s method for nonconservative hyperbolic systems. Applications to shallow-water systems. (English) Zbl 1130.76325 M2AN, Math. Model. Numer. Anal. 38, No. 5, 821-852 (2004). MSC: 76B55 76M20 65M06 35L45 35L60 PDFBibTeX XMLCite \textit{C. Parés} and \textit{M. Castro}, M2AN, Math. Model. Numer. Anal. 38, No. 5, 821--852 (2004; Zbl 1130.76325) Full Text: DOI Numdam EuDML
Andrianov, Nikolai; Warnecke, Gerald The Riemann problem for the Baer-Nunziato two-phase flow model. (English) Zbl 1115.76414 J. Comput. Phys. 195, No. 2, 434-464 (2004). MSC: 76T25 35L60 35L67 76L05 76M50 76V05 80A22 PDFBibTeX XMLCite \textit{N. Andrianov} and \textit{G. Warnecke}, J. Comput. Phys. 195, No. 2, 434--464 (2004; Zbl 1115.76414) Full Text: DOI
Fraccarollo, L.; Capart, H.; Zech, Y. A Godunov method for the computation of erosional shallow water transients. (English) Zbl 1028.76028 Int. J. Numer. Methods Fluids 41, No. 9, 951-976 (2003). MSC: 76M12 76B15 86A05 PDFBibTeX XMLCite \textit{L. Fraccarollo} et al., Int. J. Numer. Methods Fluids 41, No. 9, 951--976 (2003; Zbl 1028.76028) Full Text: DOI
Chacón Rebollo, Tomás; Domínguez Delgado, Antonio; Fernández Nieto, Enrique D. A family of stable numerical solvers for the shallow water equations with source terms. (English) Zbl 1083.76557 Comput. Methods Appl. Mech. Eng. 192, No. 1-2, 203-225 (2003). MSC: 76M12 76B15 PDFBibTeX XMLCite \textit{T. Chacón Rebollo} et al., Comput. Methods Appl. Mech. Eng. 192, No. 1--2, 203--225 (2003; Zbl 1083.76557) Full Text: DOI
Gallouët, Thierry; Hérard, Jean-Marc; Seguin, Nicolas Some approximate Godunov schemes to compute shallow-water equations with topography. (English) Zbl 1084.76540 Comput. Fluids 32, No. 4, 479-513 (2003). MSC: 76M12 76B15 PDFBibTeX XMLCite \textit{T. Gallouët} et al., Comput. Fluids 32, No. 4, 479--513 (2003; Zbl 1084.76540) Full Text: DOI
Fraccarollo, L.; Capart, H. Riemann wave description of erosional dam-break flows. (English) Zbl 1142.76344 J. Fluid Mech. 461, 183-228 (2002). MSC: 76B15 86A05 PDFBibTeX XMLCite \textit{L. Fraccarollo} and \textit{H. Capart}, J. Fluid Mech. 461, 183--228 (2002; Zbl 1142.76344) Full Text: DOI
Brufau, P.; Vázquez-Cendón, M. E.; García-Navarro, P. A numerical model for the flooding and drying of irregular domains. (English) Zbl 1094.76538 Int. J. Numer. Methods Fluids 39, No. 3, 247-275 (2002). MSC: 76M12 76B15 86A05 PDFBibTeX XMLCite \textit{P. Brufau} et al., Int. J. Numer. Methods Fluids 39, No. 3, 247--275 (2002; Zbl 1094.76538) Full Text: DOI
Zhou, J. G.; Causon, D. M.; Ingram, D. M.; Mingham, C. G. Numerical solutions of the shallow water equations with discontinuous bed topography. (English) Zbl 1040.76045 Int. J. Numer. Methods Fluids 38, No. 8, 769-788 (2002). MSC: 76M12 76M20 76B15 PDFBibTeX XMLCite \textit{J. G. Zhou} et al., Int. J. Numer. Methods Fluids 38, No. 8, 769--788 (2002; Zbl 1040.76045) Full Text: DOI
Goutal, N.; Maurel, F. A finite volume solver for 1D shallow-water equations applied to an actual river. (English) Zbl 1115.76355 Int. J. Numer. Methods Fluids 38, No. 1, 1-19 (2002). MSC: 76M12 76B15 86A05 PDFBibTeX XMLCite \textit{N. Goutal} and \textit{F. Maurel}, Int. J. Numer. Methods Fluids 38, No. 1, 1--19 (2002; Zbl 1115.76355) Full Text: DOI
Alcrudo, Francisco; Benkhaldoun, Fayssal Exact solutions to the Riemann problem of the shallow water equations with a bottom step. (English) Zbl 1048.76008 Comput. Fluids 30, No. 6, 643-671 (2001). MSC: 76B15 76M55 PDFBibTeX XMLCite \textit{F. Alcrudo} and \textit{F. Benkhaldoun}, Comput. Fluids 30, No. 6, 643--671 (2001; Zbl 1048.76008) Full Text: DOI
Vázquez-Cendón, María Elena Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. (English) Zbl 0931.76055 J. Comput. Phys. 148, No. 2, 497-526 (1999). MSC: 76M12 76M20 76B15 86A05 PDFBibTeX XMLCite \textit{M. E. Vázquez-Cendón}, J. Comput. Phys. 148, No. 2, 497--526 (1999; Zbl 0931.76055) Full Text: DOI
LeVeque, Randall J. Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm. (English) Zbl 0931.76059 J. Comput. Phys. 146, No. 1, 346-365 (1998). MSC: 76M20 76B15 76L05 35L65 PDFBibTeX XMLCite \textit{R. J. LeVeque}, J. Comput. Phys. 146, No. 1, 346--365 (1998; Zbl 0931.76059) Full Text: DOI Link