A robust and stable numerical scheme for a depth-averaged Euler system

Abstract : We propose an efficient numerical scheme for the resolution of a non-hydrostatic Saint-Venant type model. The model is a shallow water type approximation of the incompressbile Euler system with free surface and slightly differs from the Green-Naghdi model. The numerical approximation relies on a kinetic interpretation of the model and a projection-correction type scheme. The hyperbolic part of the system is approximated using a kinetic based finite volume solver and the correction step implies to solve an elliptic problem involving the non-hydrostatic part of the pressure. We prove the numerical scheme satisfies properties such as positivity, well-balancing and a fully discrete entropy inequality. The numerical scheme is confronted with various time-dependent analytical solutions. Notice that the numerical procedure remains stable when the water depth tends to zero.
Type de document :
Pré-publication, Document de travail
2015
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https://hal.inria.fr/hal-01162109
Contributeur : Jacques Sainte-Marie <>
Soumis le : lundi 14 septembre 2015 - 08:48:21
Dernière modification le : jeudi 11 janvier 2018 - 06:25:25
Document(s) archivé(s) le : vendredi 5 mai 2017 - 12:04:05

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  • HAL Id : hal-01162109, version 3
  • ARXIV : 1506.03316

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N. Aissiouene, Marie-Odile Bristeau, Edwige Godlewski, Jacques Sainte-Marie. A robust and stable numerical scheme for a depth-averaged Euler system. 2015. 〈hal-01162109v3〉

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