Cao, Yangyang; Kurganov, Alexander; Liu, Yongle Flux globalization based well-balanced path-conservative central-upwind scheme for the thermal rotating shallow water equations. (English) Zbl 07783917 Commun. Comput. Phys. 34, No. 4, 993-1042 (2023). MSC: 76M12 65M08 86-08 86-10 86A10 35L67 PDFBibTeX XMLCite \textit{Y. Cao} et al., Commun. Comput. Phys. 34, No. 4, 993--1042 (2023; Zbl 07783917) Full Text: DOI
Huang, Weizhang; Li, Ruo; Qiu, Jianxian; Zhang, Min A well-balanced moving mesh discontinuous Galerkin method for the Ripa model on triangular meshes. (English) Zbl 07690220 J. Comput. Phys. 487, Article ID 112147, 30 p. (2023). MSC: 65Mxx 76Mxx 35Lxx PDFBibTeX XMLCite \textit{W. Huang} et al., J. Comput. Phys. 487, Article ID 112147, 30 p. (2023; Zbl 07690220) Full Text: DOI arXiv
Gómez-Bueno, I.; Boscarino, S.; Castro, M. J.; Parés, C.; Russo, G. Implicit and semi-implicit well-balanced finite-volume methods for systems of balance laws. (English) Zbl 1506.65135 Appl. Numer. Math. 184, 18-48 (2023). Reviewer: Abdallah Bradji (Annaba) MSC: 65M08 65M06 65N06 65L06 76B15 76M12 76M20 PDFBibTeX XMLCite \textit{I. Gómez-Bueno} et al., Appl. Numer. Math. 184, 18--48 (2023; Zbl 1506.65135) Full Text: DOI arXiv
Dong, Jian; Qian, Xu Well-balanced and positivity-preserving surface reconstruction schemes solving Ripa systems with nonflat bottom topography. (English) Zbl 1505.76062 SIAM J. Sci. Comput. 44, No. 5, A3098-A3129 (2022). MSC: 76M12 76M20 76B10 65M08 PDFBibTeX XMLCite \textit{J. Dong} and \textit{X. Qian}, SIAM J. Sci. Comput. 44, No. 5, A3098--A3129 (2022; Zbl 1505.76062) Full Text: DOI
Berthon, Christophe; Bulteau, Solène; Foucher, Françoise; M’Baye, Meissa; Michel-Dansac, Victor A very easy high-order well-balanced reconstruction for hyperbolic systems with source terms. (English) Zbl 1501.65045 SIAM J. Sci. Comput. 44, No. 4, A2506-A2535 (2022). Reviewer: Abdallah Bradji (Annaba) MSC: 65M08 35L65 65M12 35D30 76M12 PDFBibTeX XMLCite \textit{C. Berthon} et al., SIAM J. Sci. Comput. 44, No. 4, A2506--A2535 (2022; Zbl 1501.65045) Full Text: DOI
Schneider, Kleiton A.; Gallardo, José M.; Escalante, Cipriano Efficient GPU implementation of multidimensional incomplete Riemann solvers for hyperbolic nonconservative systems: applications to shallow water systems with topography and dry areas. (English) Zbl 1492.76086 J. Sci. Comput. 92, No. 2, Paper No. 30, 42 p. (2022). MSC: 76M12 76N15 PDFBibTeX XMLCite \textit{K. A. Schneider} et al., J. Sci. Comput. 92, No. 2, Paper No. 30, 42 p. (2022; Zbl 1492.76086) Full Text: DOI
Schneider, Kleiton A.; Gallardo, José M.; Balsara, Dinshaw S.; Nkonga, Boniface; Parés, Carlos Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems. Applications to shallow water systems. (English) Zbl 07515448 J. Comput. Phys. 444, Article ID 110547, 49 p. (2021). MSC: 65Mxx 76Mxx 35Lxx PDFBibTeX XMLCite \textit{K. A. Schneider} et al., J. Comput. Phys. 444, Article ID 110547, 49 p. (2021; Zbl 07515448) Full Text: DOI
Bouchut, François; Fernández-Nieto, Enrique D.; Koné, El Hadji; Mangeney, Anne; Narbona-Reina, Gladys Dilatancy in dry granular flows with a compressible \(\mu(I)\) rheology. (English) Zbl 07500747 J. Comput. Phys. 429, Article ID 110013, 31 p. (2021). MSC: 76Txx 65Mxx 76Mxx PDFBibTeX XMLCite \textit{F. Bouchut} et al., J. Comput. Phys. 429, Article ID 110013, 31 p. (2021; Zbl 07500747) Full Text: DOI Link
Barsukow, Wasilij; Berberich, Jonas P.; Klingenberg, Christian On the active flux scheme for hyperbolic PDEs with source terms. (English) Zbl 07456294 SIAM J. Sci. Comput. 43, No. 6, A4015-A4042 (2021). MSC: 65-XX 35L65 35L45 65M08 PDFBibTeX XMLCite \textit{W. Barsukow} et al., SIAM J. Sci. Comput. 43, No. 6, A4015--A4042 (2021; Zbl 07456294) Full Text: DOI arXiv
Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael A well balanced finite volume scheme for general relativity. (English) Zbl 07456293 SIAM J. Sci. Comput. 43, No. 6, B1226-B1251 (2021). MSC: 65-XX 35L40 65M08 83C05 83C10 85-08 85-10 85A30 PDFBibTeX XMLCite \textit{E. Gaburro} et al., SIAM J. Sci. Comput. 43, No. 6, B1226--B1251 (2021; Zbl 07456293) 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
Berberich, Jonas P.; Chandrashekar, Praveen; Klingenberg, Christian High order well-balanced finite volume methods for multi-dimensional systems of hyperbolic balance laws. (English) Zbl 1521.76393 Comput. Fluids 219, Article ID 104858, 13 p. (2021). MSC: 76M12 65M08 35L65 76Nxx PDFBibTeX XMLCite \textit{J. P. Berberich} et al., Comput. Fluids 219, Article ID 104858, 13 p. (2021; Zbl 1521.76393) Full Text: DOI arXiv
Berberich, Jonas P.; Käppeli, Roger; Chandrashekar, Praveen; Klingenberg, Christian High order discretely well-balanced methods for arbitrary hydrostatic atmospheres. (English) Zbl 1490.76141 Commun. Comput. Phys. 30, No. 3, 666-708 (2021). MSC: 76M12 PDFBibTeX XMLCite \textit{J. P. Berberich} et al., Commun. Comput. Phys. 30, No. 3, 666--708 (2021; Zbl 1490.76141) Full Text: DOI arXiv
Thanh, Nguyen Xuan; Thanh, Mai Duc; Cuong, Dao Huy A well-balanced high-order scheme on van Leer-type for the shallow water equations with temperature gradient and variable bottom topography. (English) Zbl 1473.65147 Adv. Comput. Math. 47, No. 1, Paper No. 13, 53 p. (2021). Reviewer: Victor Michel-Dansac (Strasbourg) MSC: 65M08 35L65 76B15 86A05 35Q35 35Q86 PDFBibTeX XMLCite \textit{N. X. Thanh} et al., Adv. Comput. Math. 47, No. 1, Paper No. 13, 53 p. (2021; Zbl 1473.65147) Full Text: DOI
Gómez-Bueno, Irene; Castro, Manuel J.; Parés, Carlos High-order well-balanced methods for systems of balance laws: a control-based approach. (English) Zbl 1465.76062 Appl. Math. Comput. 394, Article ID 125820, 37 p. (2021). MSC: 76M12 76N15 PDFBibTeX XMLCite \textit{I. Gómez-Bueno} et al., Appl. Math. Comput. 394, Article ID 125820, 37 p. (2021; Zbl 1465.76062) Full Text: DOI
Bouchut, François; Lhébrard, Xavier Convergence of the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography. (English) Zbl 1466.65091 Math. Comput. 90, No. 329, 1119-1153 (2021). MSC: 65M08 65M12 76B15 76M12 35L65 35D30 PDFBibTeX XMLCite \textit{F. Bouchut} and \textit{X. Lhébrard}, Math. Comput. 90, No. 329, 1119--1153 (2021; Zbl 1466.65091) Full Text: DOI Link
Li, Jiaojiao; Li, Gang; Qian, Shouguo; Gao, Jinmei; Niu, Qiang A high-order well-balanced discontinuous Galerkin method based on the hydrostatic reconstruction for the Ripa model. (English) Zbl 1488.74133 Adv. Appl. Math. Mech. 12, No. 6, 1416-1437 (2020). MSC: 74S05 PDFBibTeX XMLCite \textit{J. Li} et al., Adv. Appl. Math. Mech. 12, No. 6, 1416--1437 (2020; Zbl 1488.74133) Full Text: DOI
Franck, Emmanuel; Navoret, Laurent Semi-implicit two-speed well-balanced relaxation scheme for Ripa model. (English) Zbl 1453.65249 Klöfkorn, Robert (ed.) et al., Finite volumes for complex applications IX – methods, theoretical aspects, examples. FVCA 9, Bergen, Norway, June 15–19, 2020. In 2 volumes. Volume I and II. Cham: Springer. Springer Proc. Math. Stat. 323, 735-743 (2020). MSC: 65M08 65N08 65M06 76B15 35Q31 PDFBibTeX XMLCite \textit{E. Franck} and \textit{L. Navoret}, Springer Proc. Math. Stat. 323, 735--743 (2020; Zbl 1453.65249) Full Text: DOI HAL
Kurganov, Alexander; Liu, Yongle; Zeitlin, Vladimir A well-balanced central-upwind scheme for the thermal rotating shallow water equations. (English) Zbl 1436.65123 J. Comput. Phys. 411, Article ID 109414, 23 p. (2020). MSC: 65M08 65Z05 86A05 86A10 PDFBibTeX XMLCite \textit{A. Kurganov} et al., J. Comput. Phys. 411, Article ID 109414, 23 p. (2020; Zbl 1436.65123) Full Text: DOI arXiv
Castro, Manuel J.; Parés, Carlos Well-balanced high-order finite volume methods for systems of balance laws. (English) Zbl 1440.65109 J. Sci. Comput. 82, No. 2, Paper No. 48, 48 p. (2020). MSC: 65M08 76M12 76N06 76B15 35Q31 35D30 PDFBibTeX XMLCite \textit{M. J. Castro} and \textit{C. Parés}, J. Sci. Comput. 82, No. 2, Paper No. 48, 48 p. (2020; Zbl 1440.65109) Full Text: DOI
Britton, Jolene; Xing, Yulong High order still-water and moving-water equilibria preserving discontinuous Galerkin methods for the Ripa model. (English) Zbl 1448.35386 J. Sci. Comput. 82, No. 2, Paper No. 30, 37 p. (2020). MSC: 35Q35 65M60 PDFBibTeX XMLCite \textit{J. Britton} and \textit{Y. Xing}, J. Sci. Comput. 82, No. 2, Paper No. 30, 37 p. (2020; Zbl 1448.35386) Full Text: DOI
Berberich, Jonas P.; Chandrashekar, Praveen; Klingenberg, Christian; Röpke, Friedrich K. Second order finite volume scheme for Euler equations with gravity which is well-balanced for general equations of state and grid systems. (English) Zbl 1484.76047 Commun. Comput. Phys. 26, No. 2, 599-630 (2019). MSC: 76M12 76N15 PDFBibTeX XMLCite \textit{J. P. Berberich} et al., Commun. Comput. Phys. 26, No. 2, 599--630 (2019; Zbl 1484.76047) Full Text: DOI arXiv
Rabbani, Omar; Ahmed, Munshoor; Zia, Saqib Transport of pollutant in shallow flows: a space-time CE/SE scheme. (English) Zbl 1442.65174 Comput. Math. Appl. 77, No. 12, 3195-3211 (2019). MSC: 65M06 35Q35 35Q53 76D05 92D40 PDFBibTeX XMLCite \textit{O. Rabbani} et al., Comput. Math. Appl. 77, No. 12, 3195--3211 (2019; Zbl 1442.65174) Full Text: DOI
Klingenberg, C.; Puppo, G.; Semplice, M. Arbitrary order finite volume well-balanced schemes for the Euler equations with gravity. (English) Zbl 1412.65125 SIAM J. Sci. Comput. 41, No. 2, A695-A721 (2019). MSC: 65M20 65Z05 76N15 65M08 35Q31 PDFBibTeX XMLCite \textit{C. Klingenberg} et al., SIAM J. Sci. Comput. 41, No. 2, A695--A721 (2019; Zbl 1412.65125) Full Text: DOI arXiv
Saleem, M. Rehan; Zia, Saqib; Ashraf, Waqas; Ali, Ishtiaq; Qamar, Shamsul The space-time CESE scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients. (English) Zbl 1409.76068 Comput. Math. Appl. 75, No. 3, 933-956 (2018). MSC: 76M10 65M60 76B15 35Q35 PDFBibTeX XMLCite \textit{M. R. Saleem} et al., Comput. Math. Appl. 75, No. 3, 933--956 (2018; Zbl 1409.76068) Full Text: DOI
Hernandez-Duenas, Gerardo A hybrid method to solve shallow water flows with horizontal density gradients. (English) Zbl 1395.76051 J. Sci. Comput. 73, No. 2-3, 753-782 (2017). MSC: 76M20 65M06 76B15 PDFBibTeX XMLCite \textit{G. Hernandez-Duenas}, J. Sci. Comput. 73, No. 2--3, 753--782 (2017; Zbl 1395.76051) Full Text: DOI
Bouchut, François; Lhébrard, Xavier A multi well-balanced scheme for the shallow water MHD system with topography. (English) Zbl 1371.76160 Numer. Math. 136, No. 4, 875-905 (2017). MSC: 76W05 76M12 35L65 PDFBibTeX XMLCite \textit{F. Bouchut} and \textit{X. Lhébrard}, Numer. Math. 136, No. 4, 875--905 (2017; Zbl 1371.76160) Full Text: DOI Link
Han, Xiao; Li, Gang Well-balanced finite difference WENO schemes for the ripa model. (English) Zbl 1390.76569 Comput. Fluids 134-135, 1-10 (2016). MSC: 76M20 65M06 76B15 86A05 PDFBibTeX XMLCite \textit{X. Han} and \textit{G. Li}, Comput. Fluids 134--135, 1--10 (2016; Zbl 1390.76569) Full Text: DOI
Franck, Emmanuel; Mendoza, Laura S. Finite volume scheme with local high order discretization of the hydrostatic equilibrium for the Euler equations with external forces. (English) Zbl 06646092 J. Sci. Comput. 69, No. 1, 314-354 (2016). MSC: 65-XX PDFBibTeX XMLCite \textit{E. Franck} and \textit{L. S. Mendoza}, J. Sci. Comput. 69, No. 1, 314--354 (2016; Zbl 06646092) Full Text: DOI HAL
Touma, R.; Koley, U.; Klingenberg, C. Well-balanced unstaggered central schemes for the Euler equations with gravitation. (English) Zbl 1346.76100 SIAM J. Sci. Comput. 38, No. 5, B773-B807 (2016). MSC: 76M12 65M08 35Q31 PDFBibTeX XMLCite \textit{R. Touma} et al., SIAM J. Sci. Comput. 38, No. 5, B773--B807 (2016; Zbl 1346.76100) Full Text: DOI
Chandrashekar, Praveen; Klingenberg, Christian A second order well-balanced finite volume scheme for Euler equations with gravity. (English) Zbl 1320.76078 SIAM J. Sci. Comput. 37, No. 3, B382-B402 (2015). MSC: 76M12 65N08 35L65 35Q31 76N15 PDFBibTeX XMLCite \textit{P. Chandrashekar} and \textit{C. Klingenberg}, SIAM J. Sci. Comput. 37, No. 3, B382--B402 (2015; Zbl 1320.76078) Full Text: DOI