| RWTH Publication No: 712949 2018   IGPM476.pdf
| Comparison of Different Splitting Techniques for the Isentropic Euler Equations
|Klaus Kaiser, Jonas Zeifang, Jochen Schütz, Andrea Beck, Claus-Dieter Munz
|The isentropic Euler equations at low Mach number are inherently stiff equations. To deal with them numerically, one can hardly use explicit-in-time standard methods known from the ’compressible’ world as the CFL condition dictates prohibitively small time steps. A technique that has become popular in recent years is the use of a convective flux splitting upon which stiff and non-stiff parts are identified that are then treated implicitly and explicitly, respectively.
This leads to the well-known IMEX schemes. In this paper, we investigate multiple splittings to accurately and efficiently compute the low-Mach number case of the compressible isentropic Euler equations. Temporal discretization is done with IMEX Runge-Kutta methods, while for the spatial part, we rely on the discontinuous Galerkin spectral element method. For a general class of splittings, it is shown that the fully discrete method respects the low-Mach asymptotics. Subsequently, splittings are investigated and compared numerically for several test cases.
| discontinuous Galerkin spectral element, low Mach, IMEX Runge-Kutta, flux splitting, asymptotic consistency