WELL-BALANCED SIMULATION OF GEOPHYSICAL FLOWS VIA THE SHALLOW WATER EQUATIONS WITH BOTTOM TOPOGRAPHY: CONSISTENCY AND NUMERICAL COMPUTATION

In this contribution we review a well-balancing modification for the shallow water equations and give a new result on its order of consistency, where dry regions are included. Furthermore, we combine the well-balancing modification with an existing wetting and drying approach. We show numerical results including the application to equations posed on surfaces including a realistic bottom topography. For this, we propose a finite volume scheme that is able to deal with a variety of surfaces.