We present a shock-capturing space-time Discontinuous Galerkin method to approximate all speed flows modeled by systems of conservation laws with multiple time scales. The method provides a very general and computationally efficient framework for approximating such systems on account of its ability to incorporate large time steps. Numerical examples ranging from computing the incompressible limit (robustness with respect to Mach number) ...

We describe a shock-capturing streamline diffusion space-time discontinuous Galerkin (DG) method to discretize the shallow water equations with variable bottom topography. This method, based on the entropy variables as degrees of freedom, is shown to be energy stable as well as well-balanced with respect to the lake at rest steady state. We present numerical experiments illustrating the numerical method.