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A robust structure-preserving surface reconstruction scheme for two-layer shallow water equations based on a relaxation model and an extension on adaptive moving triangles
Relationship Between Water Surface Elevation and Mean Water Depth for a Partially Wetted Rectangular Grid Cell in Numerical Simulations of Shallow Water Flows with Complex Topography
A Well-balanced Point-Average-Moment PolynomiAl-Interpreted (PAMPA) Method for Shallow Water Equations with Horizontal Temperature Gradients on Triangular Meshes
Second-Order Accurate Structure-Preserving Scheme for Solute Transport on Polygonal Meshes
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Proceedings of the Canadian Society of Civil Engineering Annual Conference 2021
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Well-Balanced and Positivity-Preserving Surface Reconstruction Schemes Solving Ripa Systems With Nonflat Bottom Topography
Well-balanced positivity preserving adaptive moving mesh central-upwind schemes for the Saint-Venant system
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Proceedings of the Canadian Society of Civil Engineering Annual Conference 2021
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Accelerating Tsunami Modeling for Evacuation Studies through Modification of the Manning Roughness Values
An adaptive central‐upwind scheme on quadtree grids for variable density shallow water equations
Mohammad A. Ghazizadeh and Abdolmajid Mohammadian International Journal for Numerical Methods in Fluids 94(5) 461 (2022) https://doi.org/10.1002/fld.5062
Numerical Approximation of Hyperbolic Systems of Conservation Laws
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Pressure-balanced Saint–Venant equations for improved asymptotic modelling of pipe flow
Adaptive Moving Mesh Central-Upwind Schemes for Hyperbolic System of PDEs: Applications to Compressible Euler Equations and Granular Hydrodynamics
Alexander Kurganov, Zhuolin Qu, Olga S. Rozanova and Tong Wu Communications on Applied Mathematics and Computation 3(3) 445 (2021) https://doi.org/10.1007/s42967-020-00082-6
An adaptive well-balanced positivity preserving central-upwind scheme on quadtree grids for shallow water equations
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
Path-conservative central-upwind schemes for nonconservative hyperbolic systems
Manuel Jesús Castro Díaz, Alexander Kurganov and Tomás Morales de Luna ESAIM: Mathematical Modelling and Numerical Analysis 53(3) 959 (2019) https://doi.org/10.1051/m2an/2018077
A robust numerical model for shallow water governing solute transport with wet/dry interfaces
A modified central discontinuous Galerkin method with positivity-preserving and well-balanced properties for the one-dimensional nonlinear shallow water equations
Well-balanced schemes for the shallow water equations with Coriolis forces
Alina Chertock, Michael Dudzinski, Alexander Kurganov and Mária Lukáčová-Medvid’ová Numerische Mathematik 138(4) 939 (2018) https://doi.org/10.1007/s00211-017-0928-0
Well-balanced positivity preserving central-upwind scheme with a novel wet/dry reconstruction on triangular grids for the Saint-Venant system
Theory, Numerics and Applications of Hyperbolic Problems I
Alina Chertock, Michael Herty and Şeyma Nur Özcan Springer Proceedings in Mathematics & Statistics, Theory, Numerics and Applications of Hyperbolic Problems I 236 345 (2018) https://doi.org/10.1007/978-3-319-91545-6_28
Three-dimensional shallow water system: A relaxation approach
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 numerical model for three-dimensional shallow water flows with sharp gradients over mobile topography
Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues
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A Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Method for the Nonlinear Shallow Water Equations
Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues
A. Kurganov Handbook of Numerical Analysis, Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues 17 525 (2016) https://doi.org/10.1016/bs.hna.2016.09.008
Well-balanced positivity preserving cell-vertex central-upwind scheme for shallow water flows
A two‐dimensional numerical scheme of dry/wet fronts for the Saint‐Venant system of shallow water equations
Zsolt Horváth, Jürgen Waser, Rui A. P. Perdigão, Artem Konev and Günter Blöschl International Journal for Numerical Methods in Fluids 77(3) 159 (2015) https://doi.org/10.1002/fld.3983
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
Well‐balanced positivity preserving central‐upwind scheme for the shallow water system with friction terms
A. Chertock, S. Cui, A. Kurganov and T. Wu International Journal for Numerical Methods in Fluids 78(6) 355 (2015) https://doi.org/10.1002/fld.4023
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
Xin Liu, Abdolmajid Mohammadian, Alexander Kurganov and Julio Angel Infante Sedano Journal of Computational Physics 300 202 (2015) https://doi.org/10.1016/j.jcp.2015.07.043
Numerical model of currents generated by sources and sinks in a circular rotating channel
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
A stable 2D unstructured shallow flow model for simulations of wetting and drying over rough terrains