{A multilayer Saint-Venant system with mass exchanges for Shallow Water flows. Derivation and numerical validation

Emmanuel Audusse 1 Marie-Odile Bristeau 2 Benoît Perthame 2, 3 Jacques Sainte-Marie 4
1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 BANG - Nonlinear Analysis for Biology and Geophysical flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
3 LJLL - Laboratoire Jacques-Louis Lions
4 MACS - Modeling, analysis and control in computational structural dynamics
Inria Paris-Rocquencourt
Abstract : The standard multilayer Saint-Venant system consists in introducing fluid layers that are advected by the interfacial velocities. As a consequence there is no mass exchanges between these layers and each layer is described by its height and its average velocity. Here we introduce another multilayer system with mass exchanges between the neighborhing layers where the unknowns are a total height of water and an average velocity per layer. We derive it from Navier-Stokes system with an hydrostatic pressure and prove energy and hyperbolicity properties of the model. We also give a kinetic interpretation leading to effective numerical schemes with positivity and energy properties. Numerical tests show the versatility of the approach and its ability to compute recirculation cases with wind forcing.
Keywords : Navier-Stokes equations Saint-Venant equations Free surface Multilayer system Kinetic scheme
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Submitted on : Friday, January 23, 2009 - 6:58:32 PM
Last modification on : Monday, March 25, 2019 - 9:00:03 AM
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  • HAL Id : hal-00355730, version 1
  • ARXIV : 0901.3887

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Emmanuel Audusse, Marie-Odile Bristeau, Benoît Perthame, Jacques Sainte-Marie. {A multilayer Saint-Venant system with mass exchanges for Shallow Water flows. Derivation and numerical validation. Modelisation Mathématique et Analyse Numérique, EDP sciences SMAI, 2009, pp.1-30. ⟨hal-00355730⟩

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