On Rosenbrock and ESDIRK methods for unsteady compressible flows

In this article, the efficiency of time adaptive Rosenbrock and ESDIRK methods is compared for finite volume discretizations for compressible unsteady viscous flows. To make the comparison fair, first an efficient solver for both classes in the JFNK context is identified, where the tolerance TOL that steers time adaptivity is the main input parameter. To specify the tolerances in the sub solver, we suggest a simple strategy for the Rosenbrock methods of using TOL/100 that is a good compromise between stability and computational effort. It turns out that the Rosenbrock methods, in particular RODASP, outperform the ESDIRK methods.