Numerical simulations of a non-hydrostatic shallow water model

• DOI: 10.1016/j.compfluid.2011.02.013
• Publication Date: 2011-03-07T22:03:12Z
• Authors: Marie-Odile Bristeau; Nicole Goutal; Jacques Sainte-Marie
• Keywords: [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]; 0101 mathematics; Navier-Stokes equations Saint-Venant equations Boussinesq equations Free surface Dispersive terms Asymptotic analysis; 01 natural sciences; [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]

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.