A well-balanced, positive, entropy-stable, and multi-dimensional-aware finite volume scheme for 2D shallow-water equations with unstructured grids
GROSSO, Alessia
Centre d'études des systèmes et des technologies avancées [CESTA]
Institut de Mathématiques de Bordeaux [IMB]
Centre d'études des systèmes et des technologies avancées [CESTA]
Institut de Mathématiques de Bordeaux [IMB]
CHAN, Agnes
Centre d'études des systèmes et des technologies avancées [CESTA]
Institut de Mathématiques de Bordeaux [IMB]
Leer más >
Centre d'études des systèmes et des technologies avancées [CESTA]
Institut de Mathématiques de Bordeaux [IMB]
GROSSO, Alessia
Centre d'études des systèmes et des technologies avancées [CESTA]
Institut de Mathématiques de Bordeaux [IMB]
Centre d'études des systèmes et des technologies avancées [CESTA]
Institut de Mathématiques de Bordeaux [IMB]
CHAN, Agnes
Centre d'études des systèmes et des technologies avancées [CESTA]
Institut de Mathématiques de Bordeaux [IMB]
< Leer menos
Centre d'études des systèmes et des technologies avancées [CESTA]
Institut de Mathématiques de Bordeaux [IMB]
Idioma
en
Document de travail - Pré-publication
Este ítem está publicado en
2023-07-13
Resumen en inglés
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 ...Leer más >
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.< Leer menos
Palabras clave en inglés
Finite volume schemes
Lagrangian Riemann solver
Eulerian Riemann solver
Shallow-water equations
Balance laws
Well-balanced scheme
Orígen
Importado de HalCentros de investigación