A subsonic-well-balanced reconstruction scheme for shallow water flows
François Bouchut and Tomás Morales de Luna
Abstract: We consider the Saint Venant system for shallow water flows with non-flat bottom. In the past years, efficient well-balanced methods have been proposed in order to well resolve solutions close to steady states at rest. Here we describe a strategy based on a local subsonic steady-state reconstruction that allows to derive a subsonic-well-balanced scheme, preserving exactly all the subsonic steady states. It generalizes the now well-known hydrostatic solver, and as the latter it preserves nonnegativity of water height and satisfies a semi-discrete entropy inequality. An application to the Euler–Poisson system is proposed.