A combined finite volume - finite element scheme for a dispersive shallow water system

Nora Aissiouene 1, 2, 3 Marie-Odile Bristeau 1, 2, 3 Edwige Godlewski 1, 2, 3 Jacques Sainte-Marie 1, 2, 3
1 LJLL - Laboratoire Jacques-Louis Lions
2 Cerema Direction Centre-Est - Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement - Direction Centre-Est
3 ANGE - Numerical Analysis, Geophysics and Ecology
LJLL - Laboratoire Jacques-Louis Lions, Inria de Paris
Abstract : We propose a variational framework for the resolution of a non-hydrostatic Saint-Venant type model with bottom topography. This model is a shallow water type approximation of the incompressible Euler system with free surface and slightly differs from the Green-Nagdhi model, see [13] for more details about the model derivation. The numerical approximation relies on a prediction-correction type scheme initially introduced by Chorin-Temam [17] to treat the incompressibility in the Navier-Stokes equations. The hyperbolic part of the system is approximated using a kinetic finite volume solver and the correction step implies to solve a mixed problem where the velocity and the pressure are defined in compatible finite element spaces. The resolution of the incompressibility constraint leads to an elliptic problem involving the non-hydrostatic part of the pressure. This step uses a variational formulation of a shallow water version of the incompressibility condition. Several numerical experiments are performed to confirm the relevance of our approach.
Keywords : numerical validation finite volume discrete entropy Dispersive terms finite element numerical scheme shallow water flows projection-correction scheme
Type de document :
Article dans une revue
Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2016, 11 (1), pp.1-27
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Dernière modification le : vendredi 31 août 2018 - 09:06:03
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  • HAL Id : hal-01160718, version 3
  • ARXIV : 1506.02881

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Nora Aissiouene, Marie-Odile Bristeau, Edwige Godlewski, Jacques Sainte-Marie. A combined finite volume - finite element scheme for a dispersive shallow water system. Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2016, 11 (1), pp.1-27. 〈hal-01160718v3〉

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