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A Well-balanced Point-Average-Moment PolynomiAl-Interpreted (PAMPA) Method for Shallow Water Equations with Horizontal Temperature Gradients on Triangular Meshes
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
Second-Order Accurate Structure-Preserving Scheme for Solute Transport on Polygonal Meshes
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Combining a Central Scheme with the Subtraction Method for Shallow Water Equations
A Very Easy High-Order Well-Balanced Reconstruction for Hyperbolic Systems with Source Terms
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Proceedings of the Canadian Society of Civil Engineering Annual Conference 2021
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Adaptive physical-constraints-preserving unstaggered central schemes for shallow water equations on quadrilateral meshes
Proceedings of the Canadian Society of Civil Engineering Annual Conference 2021
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Well-balanced positivity preserving adaptive moving mesh central-upwind schemes for the Saint-Venant system
Alexander Kurganov, Zhuolin Qu and Tong Wu ESAIM: Mathematical Modelling and Numerical Analysis 56(4) 1327 (2022) https://doi.org/10.1051/m2an/2022041
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
A structure-preserving algorithm for surface water flows with transport processes
Numerical Approximation of Hyperbolic Systems of Conservation Laws
Edwige Godlewski and Pierre-Arnaud Raviart Applied Mathematical Sciences, Numerical Approximation of Hyperbolic Systems of Conservation Laws 118 627 (2021) https://doi.org/10.1007/978-1-0716-1344-3_7
Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations
Dihan Dai, Yekaterina Epshteyn and Akil Narayan SIAM Journal on Scientific Computing 43(2) A929 (2021) https://doi.org/10.1137/20M1360736
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 modified central discontinuous Galerkin method with positivity-preserving and well-balanced properties for the one-dimensional nonlinear shallow water equations
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
Generalized Sensitivity Parameter Free Fifth Order WENO Finite Difference Scheme with Z-Type Weights
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
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
Well-balanced open boundary condition in a lattice Boltzmann model for shallow water with arbitrary bathymetry
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
Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues
Y. Xing Handbook of Numerical Analysis, Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues 18 361 (2017) https://doi.org/10.1016/bs.hna.2016.09.003
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
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
Application of positivity-preserving well-balanced discontinuous Galerkin method in computational hydrology
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
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 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
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
A robust and well-balanced numerical model for solving the two-layer shallow water equations over uneven topography
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
Development of a Cell‐Centered Godunov‐Type Finite Volume Model for Shallow Water Flow Based on Unstructured Mesh
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 kinetic scheme for the one-dimensional open channel flow equations with applications on networks