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A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation*

Published online by Cambridge University Press:  24 June 2010

Emmanuel Audusse ,
Marie-Odile Bristeau ,
Benoît Perthame  and
Jacques Sainte-Marie
Emmanuel Audusse
Affiliation:
Univ. Paris 13, Institut Galilée, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France. audusse@math.univ-paris13.fr
Marie-Odile Bristeau
Affiliation:
INRIA Paris-Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France. Marie-Odile.Bristeau@inria.fr
Benoît Perthame
Affiliation:
INRIA Paris-Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France. Marie-Odile.Bristeau@inria.fr Lab. J.-L. Lions, Univ. P. et M. Curie, BC187, 4 place Jussieu, 75252 Paris Cedex 05, France. benoit.perthame@upmc.fr
Jacques Sainte-Marie
Affiliation:
INRIA Paris-Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France. Marie-Odile.Bristeau@inria.fr Saint-Venant Laboratory, 6 quai Watier, 78400 Chatou, France. Jacques.Sainte-Marie@inria.fr
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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 neighboring 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 equationsSaint-Venant equationsfree surfacemultilayer systemkinetic scheme
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 1 , January 2011 , pp. 169 - 200
Copyright
© EDP Sciences, SMAI, 2010

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