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A well-balanced finite volume scheme based on planar Riemann solutions for 2D shallow water equations with bathymetry

Author

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  • Hoai Linh, Nguyen Ba
  • Cuong, Dao Huy

Abstract

We consider in this paper a finite volume scheme based on local planar Riemann solutions for the two-dimensional shallow water equations with bathymetry. The model involves a nonconservative term, which often makes standard schemes difficult to approximate solutions in certain regions. The scheme to be presented is a development of the preliminary works that will be cited below. Our foremost purpose is to extend those results to two-dimensional formalism while preserving the physical and mathematical properties, including the well-balancedness. The proposed scheme is applied to some specific families of solutions, especially lake at rest and partially well-balanced solution. The numerical results show that this approach can give a good accuracy, except for resonant cases. Furthermore, it is proved that our finite volume scheme can preserve the C-property in the sense that it can capture exactly the lake at rest solution.

Suggested Citation

  • Hoai Linh, Nguyen Ba & Cuong, Dao Huy, 2023. "A well-balanced finite volume scheme based on planar Riemann solutions for 2D shallow water equations with bathymetry," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    • Handle: RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003363
    DOI: 10.1016/j.amc.2023.128167
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