Résumé
We consider numerical solutions of the 2DH Non-Linear Shallow Water equations with a bed slope source term. To accurately describe the evolution of the shoreline over a strongly varying topography, we investigate a new model, called SU RF_W B. It relies on a reconstruction method for the treatment of the bed-slope and can handle strong variations of topography. The use of the recent VFRoe-ncv Riemann solver leads to a robust treatment of wetting and drying phenomena, which preserves the water depth positivity. An adapted "second order" reconstruction generates accurate bore-capturing abilities. This model is validated against analytical solutions involving a time-dependent moving shoreline and a study of mean-currents over a ridge and runnel system is investigated. This model should have an impact in time-varying numerical simulations in the surf zone.