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

Jean-Frédéric Gerbeau; Benoit Perthame

doi:10.3934/dcdsb.2001.1.89

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2001, Volume 1, Issue 1: 89-102. Doi: 10.3934/dcdsb.2001.1.89

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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

Received: November 2000

Revised: January 2001

Published: February 2001

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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.

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Mathematics Subject Classification: 35Q30, 35Q35, 76D05.

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