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The present work is devoted to the derivation of a fully well-balanced andpositivepreserving numerical scheme for the shallow water equations withCoriolis force. The first main issue consists in preserving all the steadystates, including the geostrophic equilibrium. Our strategy relies on aGodunov-type scheme with suitable source term and steady state discretisations.The second challenge lies in improving the order of the scheme while preservingthe fully well-balanced property. A modification of the classical methods isrequired since no conservative reconstruction can preserve all the steadystates in the case of rotating shallow water equations. A steady state detectoris used to overcome this matter. Some numerical experiments are presented toshow the relevance and the accuracy of both first-order and second-orderschemes.

A fully well-balanced scheme for shallow water equations with Coriolis force