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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.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-01162109
Contributor : Jacques Sainte-Marie <>
Submitted on : Monday, September 14, 2015 - 8:48:21 AM
Last modification on : Monday, December 14, 2020 - 9:44:36 AM
Long-term archiving on: : Friday, May 5, 2017 - 12:04:05 PM

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

Citation

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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