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

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.
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https://hal.inria.fr/hal-01160718
Contributor : Jacques Sainte-Marie <>
Submitted on : Tuesday, June 30, 2015 - 11:45:38 AM
Last modification on : Monday, December 14, 2020 - 9:44:39 AM
Long-term archiving on: : Tuesday, April 25, 2017 - 8:12:28 PM

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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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