A High-Order Method for Weakly Compressible Flows

Abstract

In this work, we introduce an IMEX discontinuous Galerkin solver for the weakly compressible isentropic Euler equations. The splitting needed for the IMEX temporal integration is based on the recently introduced reference solution splitting [32, 52], which makes use of the incompressible solution. We show that the overall method is asymptotic preserving. Numerical results show the performance of the algorithm which is stable under a convective CFL condition and does not show any order degradation.