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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, (,
2 Université Polytechnique de Bobo-Dioulasso, 01BP 1091 Bobo 01,
3 LAMA, UMR5127 CNRS, Université de Savoie, 73376 Le Bourget du Lac, France,

Computer Modeling in Engineering & Sciences 2009, 43(1), 27-72.


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.


Cite This Article

Narbona-Reina, G., Zabsonré, J., Fernández-Nieto, E., Bresch, D. (2009). Derivation of a Bilayer Model for Shallow Water Equations with Viscosity. Numerical Validation. CMES-Computer Modeling in Engineering & Sciences, 43(1), 27–72.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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