Modified Shallow Water Equations for significantly varying bottoms

Details Modified Shallow Water Equations for significantly varying bottoms Modified Shallow Water Equations for significantly varying bottoms

2012-02-29

arxiv.org/abs/1202.6542v1

Physics

Classical Physics

30 pages, 18 figures, 88 references. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh/

Scientific paper

In the present study we propose an modified version of the nonlinear shallow water (Saint-Venant) equations for the case when the bottom undergoes some significant variations in space and time. The model is derived from a variational principle by choosing the appropriate shallow water ansatz and imposing some constraints. Our derivation procedure does not explicitly involve any small parameter and is straightforward. The novel system is a non-dispersive, and non-hydrostatic extension of the classical Saint-Venant equations. We also propose a finite volume discretization of the obtained hyperbolic system. Several test-cases are presented to highlight the added value of the new model. Some implications to tsunami wave modelling are also discussed.

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