Project R-9206

FWO travel grant for a short stay abroad for the '13th World Congress on Computational Mechanics' from 22/07 to 27/07/2018 in New York USA (Research)

It is well-known that the Euler equations at low Mach number constitute a singularly perturbed system of equations as the speed of sound approaches infinity. 'Classical' methods known from aerodynamics tend to fail because of the stiffness in the system. In particular, approaches based on purely explicit time integration suffer from a severe CFL restriction. On the other hand, purely implicit schemes introduce an excessive amount of numerical diffusion and, because the equations are nonlinear, are algebraically more difficult to solve. A remedy suggested in recent years is the use of mixed implicit/explicit (IMEX) time integration. IMEX schemes require a suitable identification of 'stiff' (to be treated implicitly) and 'non-stiff' (to be treated explicitly) terms. This is a highly nontrivial endeavor, because the splitting dictates such important features as stability, accuracy and efficiency. In this talk, we present a recently developed splitting based on the incompressible limit solution of the Euler equations. Properties of the splitting are first discussed in a simplified, yet very instructive, ODE setting. The idea is then extended to the treatment of low Mach flows. We show that the combination of a discontinuous Galerkin scheme and IMEX time integration is asymptotically consistent, meaning that the discrete limit can be seen as an approximation to the incompressible limit. Numerical results demonstrate the behavior of the scheme.

22 July 2018 - 27 July 2018