A semi-implicit discontinuous Galerkin finite element method for the numerical solution of inviscid compressible flow

The paper is concerned with the numerical solution of an inviscid compressible flow with the aid of the discontinuous Galerkin finite element method. Since the explicit time discretization requires a high restriction of the time step, we propose semi-implicit numerical schemes based on the homogeneity of inviscid fluxes, allowing a simple linearization of the Euler equations which leads to a linear algebraic system on each time level. Numerical experiments performed for the Ringleb flow problem verify a higher order of accuracy of the presented method and demonstrate lower CPU-time costs in comparison with an explicit method. Then the method is tested on more complex unsteady Euler flows.