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

Abstract

AbstractWe 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. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)