Open Access

ARTICLE

Derivation of a Bilayer Model for Shallow Water Equations with Viscosity. Numerical Validation

G. Narbona-Reina¹, J.D.D. Zabsonré², E.D. Fernández-Nieto¹, D. Bresch³

1 Dpto. Matemática Aplicada I, E.T.S. Arquitectura. Universidad de Sevilla. Avda. Reina Mercedes 2. 41012 Sevilla, Spain, (gnarbona@us.es, edofer@us.es)
2 Université Polytechnique de Bobo-Dioulasso, 01BP 1091 Bobo 01, jzabsonre@univ-ouaga.bf
3 LAMA, UMR5127 CNRS, Université de Savoie, 73376 Le Bourget du Lac, France, Didier.Bresch@univ-savoie.fr

Computer Modeling in Engineering & Sciences 2009, 43(1), 27-72. https://doi.org/10.3970/cmes.2009.043.027

Abstract

In this work we present a new two-dimensional bilayer Shallow-Water model including viscosity and friction effects on the bottom and interface level. It is obtained following [Gerbeau and Perthame (2001)] from an asymptotic analysis of non-dimensional and incompressible Navier-Stokes equations with hydrostatic approximation. In order to obtain the viscosity effects into the model we must have into account a second order approximation. To evaluate this model we perform two numerical tests consisting of an internal dam-break problem for both, one and two dimensional cases. In the first one we make a comparison between the model obtained and the Navier-Stokes simulation.

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Keywords

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