Conservative Discretization of Coriolis Force

Abstract

In this article we are interested in the problem of numerical simulations for a shallow fluid flow in a rotating system. This problem is closely related to climate or meteorological simulations. Our purpose is to introduce a new finite volume technique which allows us to guarantee conservation of linear momentum in an inertial frame of reference. Furthermore, we show that this method introduces a new discrete Coriolis term which is based on the interface mass fluxes instead of on straightforward cell-centered evaluation of the source term. Some numerical tests exhibit that this approach significantly reduces the numerical diffusion and is particularly interesting when considering nonisotropic meshes or long time simulations.