Finite Volume Simulation of the Geostrophic Adjustment in a Rotating Shallow-Water System

The goal of this article is to simulate rotating flows of shallow layers of fluid by means of finite volume numerical schemes. More precisely, we focus on the simulation of the geostrophic adjustment phenomenon. As spatial discretization, a first order Roe-type method and some higher order extensions are developed. The time discretization is designed in order to provide suitable approximations of inertial oscillations, taking into account the hamiltonian structure of the system for these solutions. The numerical dispersion laws and the wave amplifications of the schemes are studied and their well-balanced properties are analyzed. Finally, some numerical experiments for 1d and 2d problems are shown.