 A well-balanced finite volume scheme based on planar Riemann solutions for 2D shallow water equations with bathymetryNguyen Ba Hoai Linh and Dao Huy Cuong Applied Mathematics and Computation, 2023, vol. 457, issue C 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. Keywords: Shallow water equations; Nonconservative; Riemann problem; Finite volume method; Resonant; Well-balanced scheme; Accuracy (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003363 DOI: 10.1016/j.amc.2023.128167 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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