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A well-balanced, positive, entropy-stable, and multi-dimensional-aware finite volume scheme for 2D shallow-water equations with unstructured grids

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierCentre d'études scientifiques et techniques d'Aquitaine (CESTA-CEA) [CESTA]
dc.contributor.authorDEL GROSSO, Alessia
hal.structure.identifierUniversidad de Málaga [Málaga] = University of Málaga [Málaga]
dc.contributor.authorCASTRO, Manuel
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierCentre d'études scientifiques et techniques d'Aquitaine (CESTA-CEA) [CESTA]
dc.contributor.authorCHAN, Agnes
dc.contributor.authorGALLICE, Gérard
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLOUBÈRE, Raphaël
hal.structure.identifierCentre d'études scientifiques et techniques d'Aquitaine (CESTA-CEA) [CESTA]
dc.contributor.authorMAIRE, Pierre-Henri
dc.date.issued2024
dc.identifier.issn0021-9991
dc.description.abstractEnIn this article, we present a multi-dimensional-aware Eulerian Riemann Solver (RS) and its associated Finite Volume (FV) scheme for the 2D Shallow-Water (SW) equations. This RS, appropriately derived from its associated Lagrangian version, presents the specific feature of coupling all cells in the vicinity of the current one. Consequently, this solver is no longer a 1D RS across one edge. Contrarily, it encounters for genuine multidimensional effects and for the presence of the source term of the SW equations. The associated first order FV numerical scheme ensures well-balancing for lake at rest steady states, positivity preservation and entropy stability properties. Moreover, a second-order accurate extension is proposed based on Runge-Kutta time discretization and piecewise linear limited reconstructions, that preserve the well-balanced character of the first order scheme. We present several 2D tests assessing the good behaviors of the obtained numerical scheme on unstructured mesh. The numerical scheme seems insensitive to spurious numerical instabilities such as the carbuncle effect.
dc.language.isoen
dc.publisherElsevier
dc.subject.enLagrangian Riemann solver
dc.subject.enEulerian Riemann solver
dc.subject.enShallow-water equations
dc.subject.enBalance laws
dc.subject.enWell-balanced scheme
dc.subject.enFinite volume schemes
dc.title.enA well-balanced, positive, entropy-stable, and multi-dimensional-aware finite volume scheme for 2D shallow-water equations with unstructured grids
dc.typeArticle de revue
dc.identifier.doi10.1016/j.jcp.2024.112829
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
bordeaux.journalJournal of Computational Physics
bordeaux.page112829
bordeaux.volume503
bordeaux.peerReviewedoui
hal.identifierhal-04526335
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04526335v1
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