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September 2004 Gravity driven shallow water models for arbitrary topography
Francois Bouchut, Michael Westdickenberg
Commun. Math. Sci. 2(3): 359-389 (September 2004).


We derive new models for gravity driven shallow water flows in several space dimensions over a general topography. A first model is valid for small slope variation, i.e. small curvature, and a second model is valid for arbitrary topography. In both cases no particular assumption is made on the velocity profile in the material layer. The models are written for an arbitrary coordinate system, and several formulations are provided. A Coulomb friction term is derived within the same framework, relevant in particular for debris avalanches. All our models are invariant under rotation, admit a conservative energy equation, and preserve the steady state of a lake at rest.


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Francois Bouchut. Michael Westdickenberg. "Gravity driven shallow water models for arbitrary topography." Commun. Math. Sci. 2 (3) 359 - 389, September 2004.


Published: September 2004
First available in Project Euclid: 3 March 2005

zbMATH: 1084.76012
MathSciNet: MR2118849

Rights: Copyright © 2004 International Press of Boston

Vol.2 • No. 3 • September 2004
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