Numerical simulations of a non-hydrostatic Shallow Water model
Résumé
For geophysical flows, the Saint-Venant system is often a good approximation of the Navier-Stokes equa- tions and so it is widely used for the simulations of shallow water flows and gravity waves. But the Saint- Venant system fails to represent the non-hydrostatic effects such as those associated for example with dispersive waves. To overcome this limitation, we propose an extended version of the Saint-Venant sys- tem and an associated finite volume scheme for the numerical simulations. The proposed model has sev- eral interesting properties e.g. it admits an energy balance and it preserves the dynamics of solitary waves. Several numerical results are given and especially comparisons between simulations and exper- imental measurements.