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
Solán-Fustero, P.; Gracia, J. L.; Navas-Montilla, A.; García-Navarro, P. Development of POD-based reduced order models applied to shallow water equations using augmented Riemann solvers. (English) Zbl 07737598 Comput. Methods Appl. Mech. Eng. 410, Article ID 116038, 27 p. (2023). MSC: 76-XX 92-XX PDFBibTeX XMLCite \textit{P. Solán-Fustero} et al., Comput. Methods Appl. Mech. Eng. 410, Article ID 116038, 27 p. (2023; Zbl 07737598) Full Text: DOI
Boscheri, Walter; Tavelli, Maurizio; Castro, Cristóbal E. An all Froude high order IMEX scheme for the shallow water equations on unstructured Voronoi meshes. (English) Zbl 07699012 Appl. Numer. Math. 185, 311-335 (2023). MSC: 65Mxx 76Mxx 76Bxx PDFBibTeX XMLCite \textit{W. Boscheri} et al., Appl. Numer. Math. 185, 311--335 (2023; Zbl 07699012) Full Text: DOI arXiv
Tkachenko, Sergey; Gavrilyuk, Sergey; Massoni, Jacques Extended Lagrangian approach for the numerical study of multidimensional dispersive waves: applications to the Serre-Green-Naghdi equations. (English) Zbl 07652801 J. Comput. Phys. 477, Article ID 111901, 25 p. (2023). MSC: 65Mxx 76Bxx 76Mxx PDFBibTeX XMLCite \textit{S. Tkachenko} et al., J. Comput. Phys. 477, Article ID 111901, 25 p. (2023; Zbl 07652801) Full Text: DOI arXiv
Carlino, Michele Giuliano; Gaburro, Elena Well balanced finite volume schemes for shallow water equations on manifolds. (English) Zbl 1511.76060 Appl. Math. Comput. 441, Article ID 127676, 25 p. (2023). MSC: 76M12 65M08 65M06 74S20 76M20 PDFBibTeX XMLCite \textit{M. G. Carlino} and \textit{E. Gaburro}, Appl. Math. Comput. 441, Article ID 127676, 25 p. (2023; Zbl 1511.76060) Full Text: DOI arXiv
Nordström, Jan; Winters, Andrew R. A linear and nonlinear analysis of the shallow water equations and its impact on boundary conditions. (English) Zbl 07536758 J. Comput. Phys. 463, Article ID 111254, 15 p. (2022). MSC: 65Mxx 35Lxx 76Mxx PDFBibTeX XMLCite \textit{J. Nordström} and \textit{A. R. Winters}, J. Comput. Phys. 463, Article ID 111254, 15 p. (2022; Zbl 07536758) Full Text: DOI arXiv
Ferrari, Alessia; Vacondio, Renato An augmented HLLEM ADER numerical model parallel on GPU for the porous shallow water equations. (English) Zbl 1521.76419 Comput. Fluids 238, Article ID 105360, 12 p. (2022). MSC: 76M12 65M08 65Y05 65Y10 76S05 PDFBibTeX XMLCite \textit{A. Ferrari} and \textit{R. Vacondio}, Comput. Fluids 238, Article ID 105360, 12 p. (2022; Zbl 1521.76419) 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
Ivanova, Kseniya; Caviezel, Andrin; Bühler, Yves; Bartelt, Perry Numerical modelling of turbulent geophysical flows using a hyperbolic shear shallow water model: application to powder snow avalanches. (English) Zbl 1521.76892 Comput. Fluids 233, Article ID 105211, 9 p. (2022). MSC: 76U60 86A08 PDFBibTeX XMLCite \textit{K. Ivanova} et al., Comput. Fluids 233, Article ID 105211, 9 p. (2022; Zbl 1521.76892) 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
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
Kurganov, Alexander; Liu, Yongle; Zeitlin, Vladimir Numerical dissipation switch for two-dimensional central-upwind schemes. (English) Zbl 1485.76058 ESAIM, Math. Model. Numer. Anal. 55, No. 3, 713-734 (2021). MSC: 76M12 76N15 76U05 PDFBibTeX XMLCite \textit{A. Kurganov} et al., ESAIM, Math. Model. Numer. Anal. 55, No. 3, 713--734 (2021; Zbl 1485.76058) Full Text: DOI
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
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
De Vita, Francesco; Lagrée, Pierre-Yves; Chibbaro, Sergio; Popinet, Stéphane Beyond shallow water: appraisal of a numerical approach to hydraulic jumps based upon the boundary layer theory. (English) Zbl 1477.76029 Eur. J. Mech., B, Fluids 79, 233-246 (2020). MSC: 76D10 76M99 86A05 PDFBibTeX XMLCite \textit{F. De Vita} et al., Eur. J. Mech., B, Fluids 79, 233--246 (2020; Zbl 1477.76029) Full Text: DOI HAL
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
Denissen, I. F. C.; Weinhart, T.; Te Voortwis, A.; Luding, S.; Gray, J. M. N. T.; Thornton, A. R. Bulbous head formation in bidisperse shallow granular flow over an inclined plane. (English) Zbl 1415.76708 J. Fluid Mech. 866, 263-297 (2019). MSC: 76T25 PDFBibTeX XMLCite \textit{I. F. C. Denissen} et al., J. Fluid Mech. 866, 263--297 (2019; Zbl 1415.76708) Full Text: DOI
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
Fernández-Pato, J.; Morales-Hernández, M.; García-Navarro, P. Implicit finite volume simulation of 2D shallow water flows in flexible meshes. (English) Zbl 1439.76108 Comput. Methods Appl. Mech. Eng. 328, 1-25 (2018). MSC: 76M12 65M08 65M12 76D05 PDFBibTeX XMLCite \textit{J. Fernández-Pato} et al., Comput. Methods Appl. Mech. Eng. 328, 1--25 (2018; Zbl 1439.76108) Full Text: DOI Link
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
Herbin, Raphaèle; Latché, Jean-Claude; Nguyen, Trung Tan Consistent segregated staggered schemes with explicit steps for the isentropic and full Euler equations. (English) Zbl 1405.35149 ESAIM, Math. Model. Numer. Anal. 52, No. 3, 893-944 (2018). MSC: 35Q31 65N12 65M12 76M10 76M12 PDFBibTeX XMLCite \textit{R. Herbin} et al., ESAIM, Math. Model. Numer. Anal. 52, No. 3, 893--944 (2018; Zbl 1405.35149) Full Text: DOI HAL
Aguillon, Nina; Audusse, Emmanuel; Godlewski, Edwige; Parisot, Martin Analysis of the Riemann problem for a shallow water model with two velocities. (English) Zbl 1403.35224 SIAM J. Math. Anal. 50, No. 5, 4861-4888 (2018). MSC: 35Q35 35L40 35L67 76L05 76B03 76B07 PDFBibTeX XMLCite \textit{N. Aguillon} et al., SIAM J. Math. Anal. 50, No. 5, 4861--4888 (2018; Zbl 1403.35224) 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
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
Navas-Montilla, A.; Murillo, J. Overcoming numerical shockwave anomalies using energy balanced numerical schemes. Application to the shallow water equations with discontinuous topography. (English) Zbl 1376.76034 J. Comput. Phys. 340, 575-616 (2017). MSC: 76M12 35L65 PDFBibTeX XMLCite \textit{A. Navas-Montilla} and \textit{J. Murillo}, J. Comput. Phys. 340, 575--616 (2017; Zbl 1376.76034) Full Text: DOI Link
Michel-Dansac, Victor; Berthon, Christophe; Clain, Stéphane; Foucher, Françoise A well-balanced scheme for the shallow-water equations with topography or Manning friction. (English) Zbl 1375.35389 J. Comput. Phys. 335, 115-154 (2017). MSC: 35Q35 76M12 PDFBibTeX XMLCite \textit{V. Michel-Dansac} et al., J. Comput. Phys. 335, 115--154 (2017; Zbl 1375.35389) Full Text: DOI HAL
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
Favrie, N.; Gavrilyuk, S. A rapid numerical method for solving Serre-Green-Naghdi equations describing long free surface gravity waves. (English) Zbl 1432.65120 Nonlinearity 30, No. 7, 2718-2736 (2017). MSC: 65M06 35L65 35Q53 PDFBibTeX XMLCite \textit{N. Favrie} and \textit{S. Gavrilyuk}, Nonlinearity 30, No. 7, 2718--2736 (2017; Zbl 1432.65120) Full Text: DOI
Jeschke, Anja; Vater, Stefan; Behrens, Jörn A discontinuous Galerkin method for non-hydrostatic shallow water flows. (English) Zbl 1365.76158 Cancès, Clément (ed.) et al., Finite volumes for complex applications VIII – hyperbolic, elliptic and parabolic problems. FVCA 8, Lille, France, June 12–16, 2017. Cham: Springer (ISBN 978-3-319-57393-9/hbk; 978-3-319-57394-6/ebook; 978-3-319-58818-6/set). Springer Proceedings in Mathematics & Statistics 200, 247-255 (2017). MSC: 76M12 76M10 65M60 65M08 35Q86 86-08 PDFBibTeX XMLCite \textit{A. Jeschke} et al., Springer Proc. Math. Stat. 200, 247--255 (2017; Zbl 1365.76158) Full Text: DOI
Aghakhani, Hossein; Dalbey, Keith; Salac, David; Patra, Abani K. Heuristic and Eulerian interface capturing approaches for shallow water type flow and application to granular flows. (English) Zbl 1423.76476 Comput. Methods Appl. Mech. Eng. 304, 243-264 (2016). MSC: 76T25 74E20 76M20 PDFBibTeX XMLCite \textit{H. Aghakhani} et al., Comput. Methods Appl. Mech. Eng. 304, 243--264 (2016; Zbl 1423.76476) Full Text: DOI
Lacasta, A.; García-Navarro, P. A GPU accelerated adjoint-based optimizer for inverse modeling of the two-dimensional shallow water equations. (English) Zbl 1390.76464 Comput. Fluids 136, 371-383 (2016). MSC: 76M12 65M08 65Y10 76D05 PDFBibTeX XMLCite \textit{A. Lacasta} and \textit{P. García-Navarro}, Comput. Fluids 136, 371--383 (2016; Zbl 1390.76464) Full Text: DOI
Pongsanguansin, Thida; Maleewong, Montri; Mekchay, Khamron Shallow-water simulations by a well-balanced WAF finite volume method: a case study to the great flood in 2011, Thailand. (English) Zbl 1386.86005 Comput. Geosci. 20, No. 6, 1269-1285 (2016). MSC: 86-08 86A05 76M10 76B75 PDFBibTeX XMLCite \textit{T. Pongsanguansin} et al., Comput. Geosci. 20, No. 6, 1269--1285 (2016; Zbl 1386.86005) 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
Navas-Montilla, A.; Murillo, J. Asymptotically and exactly energy balanced augmented flux-ADER schemes with application to hyperbolic conservation laws with geometric source terms. (English) Zbl 1349.65379 J. Comput. Phys. 317, 108-147 (2016). MSC: 65M08 76M12 PDFBibTeX XMLCite \textit{A. Navas-Montilla} and \textit{J. Murillo}, J. Comput. Phys. 317, 108--147 (2016; Zbl 1349.65379) Full Text: DOI Link
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
Gunawan, P. H.; Eymard, R.; Pudjaprasetya, S. R. Staggered scheme for the Exner-shallow water equations. (English) Zbl 1391.76725 Comput. Geosci. 19, No. 6, 1197-1206 (2015). MSC: 76S05 86A05 86-08 76M12 65M08 PDFBibTeX XMLCite \textit{P. H. Gunawan} et al., Comput. Geosci. 19, No. 6, 1197--1206 (2015; Zbl 1391.76725) 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
Navas-Montilla, A.; Murillo, J. Energy balanced numerical schemes with very high order. The augmented Roe flux ADER scheme. Application to the shallow water equations. (English) Zbl 1349.76372 J. Comput. Phys. 290, 188-218 (2015). MSC: 76M12 65M08 76D05 PDFBibTeX XMLCite \textit{A. Navas-Montilla} and \textit{J. Murillo}, J. Comput. Phys. 290, 188--218 (2015; Zbl 1349.76372) Full Text: DOI
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
Liu, Youqiong; Feng, Jianhu; Ren, Jiong High resolution, entropy-consistent scheme using flux limiter for hyperbolic systems of conservation laws. (English) Zbl 1434.76079 J. Sci. Comput. 64, No. 3, 914-937 (2015). MSC: 76M12 76N15 76L05 PDFBibTeX XMLCite \textit{Y. Liu} et al., J. Sci. Comput. 64, No. 3, 914--937 (2015; Zbl 1434.76079) Full Text: DOI
Hou, Jingming; Liang, Qiuhua; Zhang, Hongbin; Hinkelmann, Reinhard Multislope MUSCL method applied to solve shallow water equations. (English) Zbl 1369.35062 Comput. Math. Appl. 68, No. 12, Part A, 2012-2027 (2014). MSC: 35Q35 76M12 PDFBibTeX XMLCite \textit{J. Hou} et al., Comput. Math. Appl. 68, No. 12, Part A, 2012--2027 (2014; Zbl 1369.35062) 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
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
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
Cea, L.; Vázquez-Cendón, M. E. Unstructured finite volume discretisation of bed friction and convective flux in solute transport models linked to the shallow water equations. (English) Zbl 1402.76077 J. Comput. Phys. 231, No. 8, 3317-3339 (2012). MSC: 76M12 76D05 65M08 PDFBibTeX XMLCite \textit{L. Cea} and \textit{M. E. Vázquez-Cendón}, J. Comput. Phys. 231, No. 8, 3317--3339 (2012; Zbl 1402.76077) 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
Zokagoa, Jean-Marie; Soulaïmani, Azzeddine Modeling of wetting-drying transitions in free surface flows over complex topographies. (English) Zbl 1231.76184 Comput. Methods Appl. Mech. Eng. 199, No. 33-36, 2281-2304 (2010). MSC: 76M12 76B10 76T10 86A05 PDFBibTeX XMLCite \textit{J.-M. Zokagoa} and \textit{A. Soulaïmani}, Comput. Methods Appl. Mech. Eng. 199, No. 33--36, 2281--2304 (2010; Zbl 1231.76184) Full Text: DOI
Bernard, P.-E.; Remacle, J.-F.; Comblen, R.; Legat, V.; Hillewaert, K. High-order discontinuous Galerkin schemes on general 2D manifolds applied to the shallow water equations. (English) Zbl 1261.76026 J. Comput. Phys. 228, No. 17, 6514-6535 (2009). MSC: 76M25 65M60 PDFBibTeX XMLCite \textit{P. E. Bernard} et al., J. Comput. Phys. 228, No. 17, 6514--6535 (2009; Zbl 1261.76026) 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
George, David L. Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation. (English) Zbl 1329.76204 J. Comput. Phys. 227, No. 6, 3089-3113 (2008). MSC: 76M12 86A05 65M60 35L65 PDFBibTeX XMLCite \textit{D. L. George}, J. Comput. Phys. 227, No. 6, 3089--3113 (2008; Zbl 1329.76204) 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
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
Audusse, Emmanuel; Bouchut, François; Bristeau, Marie-Odile; Klein, Rupert; Perthame, Benoît A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. (English) Zbl 1133.65308 SIAM J. Sci. Comput. 25, No. 6, 2050-2065 (2004). MSC: 65M12 76M12 35L65 PDFBibTeX XMLCite \textit{E. Audusse} et al., SIAM J. Sci. Comput. 25, No. 6, 2050--2065 (2004; Zbl 1133.65308) 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
Toro, E. F.; Titarev, V. A. Solution of the generalized Riemann problem for advection-reaction equations. (English) Zbl 1019.35061 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No. 2018, 271-281 (2002). Reviewer: Mária Lukáčová (Brno) MSC: 35L60 35L45 PDFBibTeX XMLCite \textit{E. F. Toro} and \textit{V. A. Titarev}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No. 2018, 271--281 (2002; Zbl 1019.35061) 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
Zhou, J. G.; Causon, D. M.; Mingham, C. G.; Ingram, D. M. The surface gradient method for the treatment of source terms in the shallow-water equations. (English) Zbl 1074.86500 J. Comput. Phys. 168, No. 1, 1-25 (2001). MSC: 86-08 76M25 86A05 PDFBibTeX XMLCite \textit{J. G. Zhou} et al., J. Comput. Phys. 168, No. 1, 1--25 (2001; Zbl 1074.86500) 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