Numerical simulations of a non-hydrostatic shallow water model

For geophysical flows, the Saint-Venant system is often a good approximation of the Navier–Stokes equations 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 system and an associated finite volume scheme for the numerical simulations. The proposed model has several 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 experimental measurements.