Shallow water equations for large topographies
Résumé
In this study, we propose an improved version of nonlinear shallow water or Saint-Venant equations. The improvement is achieved by including the fluid particles vertical acceleration effect due to the variable bathymetry. More precisely, our model is not hydrostatic at the bottom. This modification is particularly pertinent when the bottom undergoes strong variations in space and/or in time. The model is derived from the relaxed variational principle by choosing the appropriate shallow water ansatz and imposing some constraints. Our derivation procedure does not explicitly involve any small parameter.
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