A fully well-balanced scheme for shallow water equations with Coriolis force
Vivien Desveaux, Alice Masset
Abstract
The present work is devoted to the derivation of a fully well-balanced and\npositivepreserving numerical scheme for the shallow water equations with\nCoriolis force. The first main issue consists in preserving all the steady\nstates, including the geostrophic equilibrium. Our strategy relies on a\nGodunov-type scheme with suitable source term and steady state discretisations.\nThe second challenge lies in improving the order of the scheme while preserving\nthe fully well-balanced property. A modification of the classical methods is\nrequired since no conservative reconstruction can preserve all the steady\nstates in the case of rotating shallow water equations. A steady state detector\nis used to overcome this matter. Some numerical experiments are presented to\nshow the relevance and the accuracy of both first-order and second-order\nschemes.\n