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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

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

Pages: 89 - 102, Volume 1, Issue 1, February 2001

doi:10.3934/dcdsb.2001.1.89       Abstract        Full Text (239.9K)       Related Articles

Jean-Frédéric Gerbeau - INRIA- Project M3N, Rocquencort B.P. 105, F-78153 Le Chesnay Cedex, France (email)
Benoit Perthame - INRIA- Project M3N, Rocquencort B.P. 105, F-78153 Le Chesnay Cedex, France (email)

Abstract: 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:  Navier-Stokes equations, Saint-Venant equations, shallow water, free surface, asymptotic analysis, viscosity, friction.
Mathematics Subject Classification:  35Q30, 35Q35, 76D05.

Received: November 2000;      Revised: January 2001;      Published: January 2001.