Adopting (s)EPIRK schemes in a domain-based IMEX setting

The simulation of viscous, compressible flows around complex geometries or similar applications often inherit the task of solving large, stiff systems of ODEs. Domain-based implicit-explicit (IMEX) type schemes offer the possibility to apply two different schemes to different parts of the computational domain. The goal hereby is to decrease the computational cost by increasing the admissible step sizes with no loss of stability and by reducing the system sizes of the linear solver within the implicit integrator. But which combination of methods reaches the largest gain in efficiency? Coupling of Runge-Kutta methods or different multistep methods has been investigated so far by other authors. Here, we inspect the adoption of the recently introduced exponential integrators called EPIRK and sEPIRK in the IMEX setting, since they are perfectly suited for large, stiff systems of ODEs.