A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation*
Univ. Paris 13, Institut Galilée, 99 avenue
Jean-Baptiste Clément, 93430 Villetaneuse, France.
2 INRIA Paris-Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France. Marie-Odile.Bristeau@inria.fr
3 Lab. J.-L. Lions, Univ. P. et M. Curie, BC187, 4 place Jussieu, 75252 Paris Cedex 05, France. firstname.lastname@example.org
4 Saint-Venant Laboratory, 6 quai Watier, 78400 Chatou, France. Jacques.Sainte-Marie@inria.fr
Revised: 15 December 2009
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.
Mathematics Subject Classification: 35Q30 / 35Q35 / 76D05
Key words: Navier-Stokes equations / Saint-Venant equations / free surface / multilayer system / kinetic scheme
This work has been achieved while the authors were involved in the ANR project METHODE (http://methode.netcipia.net).
© EDP Sciences, SMAI, 2010