A well-balanced, positive, entropy-stable, and multi-dimensional-aware finite volume scheme for 2D shallow-water equations with unstructured grids
DEL GROSSO, Alessia
Institut de Mathématiques de Bordeaux [IMB]
Centre d'études scientifiques et techniques d'Aquitaine [CESTA]
Institut de Mathématiques de Bordeaux [IMB]
Centre d'études scientifiques et techniques d'Aquitaine [CESTA]
CHAN, Agnes
Institut de Mathématiques de Bordeaux [IMB]
Centre d'études scientifiques et techniques d'Aquitaine [CESTA]
Leer más >
Institut de Mathématiques de Bordeaux [IMB]
Centre d'études scientifiques et techniques d'Aquitaine [CESTA]
DEL GROSSO, Alessia
Institut de Mathématiques de Bordeaux [IMB]
Centre d'études scientifiques et techniques d'Aquitaine [CESTA]
Institut de Mathématiques de Bordeaux [IMB]
Centre d'études scientifiques et techniques d'Aquitaine [CESTA]
CHAN, Agnes
Institut de Mathématiques de Bordeaux [IMB]
Centre d'études scientifiques et techniques d'Aquitaine [CESTA]
< Leer menos
Institut de Mathématiques de Bordeaux [IMB]
Centre d'études scientifiques et techniques d'Aquitaine [CESTA]
Idioma
en
Article de revue
Este ítem está publicado en
Journal of Computational Physics. 2024, vol. 503, p. 112829
Elsevier
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 (SW) equations. This RS, appropriately derived from its associated ...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 (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.< Leer menos
Palabras clave en inglés
Lagrangian Riemann solver
Eulerian Riemann solver
Shallow-water equations
Balance laws
Well-balanced scheme
Finite volume schemes
Orígen
Importado de HalCentros de investigación