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arXiv · 1506.03316

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

N. Aissiouene·M. -O. Bristeau·E. Godlewski·J. Sainte-Marie
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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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N. Aissiouene, M. -O. Bristeau, E. Godlewski, J. Sainte-Marie. 2015-06-10. A robust and stable numerical scheme for a depth-averaged Euler system. https://arxiv.org/abs/1506.03316

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