Efficient Time Integration of IMEX Type using Exponential Integrators for Compressible, Viscous Flow Simulation

We investigate the adaption of the recently developed exponential integrators called EPIRK in the so-called domain-based implicit-explicit (IMEX) setting of spatially discretized PDE's. The EPIRK schemes were shown to be efficient for sufficiently stiff problems and offer high precision and good stability properties like A- and L-stability in theory. In practice, however, we can show that these stability properties are dependent on the parameters of the interior approximation techniques.

Here, we introduce the IMEX-EPIRK method, which consists of coupling an explicit Runge-Kutta scheme with an EPIRK scheme. We briefly analyze its linear stability, show its conservation property and set up a CFL condition. Though the method is convergent of only first order, it demonstrates the advantages of this novel type of schemes for stiff problems very well.