Efficient computation of all speed flows using an entropy stable shock-capturing space-time discontinuous Galerkin method

Abstract

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) of the Euler equations to accelerating convergence to steady state are presented for illustrating the method.