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A well-balanced and positivity-preserving SPH method for shallow water flows in open channels
Adaptive Moving Mesh Central-Upwind Schemes for Hyperbolic System of PDEs: Applications to Compressible Euler Equations and Granular Hydrodynamics
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A New Approach for Designing Moving-Water Equilibria Preserving Schemes for the Shallow Water Equations
Yuanzhen Cheng, Alina Chertock, Michael Herty, Alexander Kurganov and Tong Wu Journal of Scientific Computing 80(1) 538 (2019) https://doi.org/10.1007/s10915-019-00947-w
One-Dimensional/Two-Dimensional Coupling Approach with Quadrilateral Confluence Region for Modeling River Systems
Well-balanced schemes for the shallow water equations with Coriolis forces
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Xin Liu, Abdolmajid Mohammadian, Julio Ángel Infante Sedano and Alexander Kurganov Journal of Computational Physics 333 160 (2017) https://doi.org/10.1016/j.jcp.2016.12.030
A positivity preserving and well-balanced DG scheme using finite volume subcells in almost dry regions
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A Well-Balanced Finite Volume Scheme for a Mixed Hyperbolic/Parabolic System to Model Chemotaxis
A two‐dimensional numerical scheme of dry/wet fronts for the Saint‐Venant system of shallow water equations
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An efficient splitting technique for two-layer shallow-water model
Christophe Berthon, Françoise Foucher and Tomás Morales Numerical Methods for Partial Differential Equations 31(5) 1396 (2015) https://doi.org/10.1002/num.21949
Well-balanced central-upwind scheme for a fully coupled shallow water system modeling flows over erodible bed
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A robust coupled 2-D model for rapidly varying flows over erodible bed using central-upwind method with wetting and drying
Xin Liu, Julio Angel Infante Sedano and Abdolmajid Mohammadian Canadian Journal of Civil Engineering 42(8) 530 (2015) https://doi.org/10.1139/cjce-2014-0524
Recent advances on the discontinuous Galerkin method for shallow water equations with topography source terms
A robust well-balanced model on unstructured grids for shallow water flows with wetting and drying over complex topography
Jingming Hou, Franz Simons, Mohamed Mahgoub and Reinhard Hinkelmann Computer Methods in Applied Mechanics and Engineering 257 126 (2013) https://doi.org/10.1016/j.cma.2013.01.015
On the well-balanced numerical discretization of shallow water equations on unstructured meshes