Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation

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February 2001, 1(1): 89-102. doi: 10.3934/dcdsb.2001.1.89

Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation

Jean-Frédéric Gerbeau ^1, and Benoit Perthame ^1,

1.	INRIA- Project M3N, Rocquencort B.P. 105, F-78153 Le Chesnay Cedex, France, France

Received November 2000 Revised January 2001 Published January 2001

Abstract
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We derive the Saint-Venant system for the shallow waters including small friction, viscosity and Coriolis-Boussinesq factor departing from the Navier-Stokes system with a free moving boundary. This derivation relies on the hydrostatic approximation where we follow the role of viscosity and friction on the bottom. Numerical comparisons between the limiting Saint-Venant system and direct Navier-Stokes simulation allow to validate this derivation.

Keywords: asymptotic analysis, friction., Navier-Stokes equations, Saint-Venant equations, shallow water, viscosity, free surface.

Mathematics Subject Classification: 35Q30, 35Q35, 76D0.

Citation: Jean-Frédéric Gerbeau, Benoit Perthame. Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation. Discrete & Continuous Dynamical Systems - B, 2001, 1 (1) : 89-102. doi: 10.3934/dcdsb.2001.1.89

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