This contribution compares the efficiency of Rosenbrock time integration
schemes with ESDIRK schemes, applicable to unsteady flow and fluid-structure interaction
simulations. Compared to non-linear ESDIRK schemes, the linear implicit Rosenbrock-
Wanner schemes require subsequent solution of the same linear systems with different
right hand sides. By solving the linear systems with the iterative solver GMRES, the preconditioner
can be reused for the subsequent stages of the Rosenbrock-Wanner scheme.
Unsteady flow simulations show a gain in computational efficiency of approximately factor
three to five in comparison with ESDIRK