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May  2005, 5(2): 189-214. doi: 10.3934/dcdsb.2005.5.189

A multilayer Saint-Venant model: Derivation and numerical validation

E. Audusse 1,

1. 

INRIA Rocquencourt, Domaine de Voluceau BP 105, 78153 Le Chesnay, France

Received  October 2003 Revised  July 2004 Published  February 2005

We introduce a new variant of the multilayer Saint-Venant system. The classical Saint-Venant system is a well-known approximation of the incompressible Navier-Stokes equations for shallow water flows with free moving boundary. Its efficiency, robustness and low computational cost make it very commonly used. Nevertheless its range of application is limited and it does not allow to access to the vertical profile of the horizontal velocity. Hence and thanks to a precise analysis of the shallow water assumption we propose here a new approximation of the Navier-Stokes equations which consists in a set of coupled Saint-Venant systems, extends the range of validity and gives a precise description of the vertical profile of the horizontal velocity while preserving the computational efficiency of the classical Saint-Venant system. We validate the model through some numerical examples.
Keywords: viscosity., shallow water assumption, Free surface Navier-Stokes equations, hy-drostatic approximation, multilayer model, Saint-Venant system.
Mathematics Subject Classification: 35Q30, 35Q35, 76D0.
Citation: E. Audusse. A multilayer Saint-Venant model: Derivation and numerical validation. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 189-214. doi: 10.3934/dcdsb.2005.5.189
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