Numerical approximation of the shallow water equations with coriolis source term

We investigate in this work a class of numerical schemes dedicated to the non-linear Shallow Water equations with topography and Coriolis force. The proposed algorithms rely on Finite Volume approximations formulated collocated staggered meshes, involving appropriate diffusion terms fluxes, expressed as discrete versions linear geostrophic balance. It follows that, contrary standard Finite-Volume approaches, provide relevant approximation equilibrium. also show that resulting methods ensure semi-discrete energy estimates. Numerical experiments exhibit efficiency approach presence force close balance, especially at low Froude number regimes.