GROSSO, Alessia; CASTRO, Manuel; CHAN, Agnes; GALLICE, Gérard; LOUBÈRE, Raphaël; MAIRE, Pierre-Henri

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GROSSO, Alessia
Centre d'études des systèmes et des technologies avancées [CESTA]
Institut de Mathématiques de Bordeaux [IMB]

CASTRO, Manuel
Universidad de Málaga [Málaga] = University of Málaga [Málaga]

CHAN, Agnes
Centre d'études des systèmes et des technologies avancées [CESTA]
Institut de Mathématiques de Bordeaux [IMB]

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2023-07-13

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In this article, we present a multi-dimensional-aware Eulerian Riemann solver (RS) and its associated finite volume (FV) scheme for the 2D shallow-water 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-balanced 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.< Réduire

Mots clés en anglais

Finite volume schemes

Lagrangian Riemann solver

Eulerian Riemann solver

Shallow-water equations

Balance laws

Well-balanced scheme

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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

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