A preconditioned Krylov technique for global hydrodynamic stability analysis of large-scale compressible flows

The combination of iterative Krylov-based eigenvalue algorithms and direct numerical simulations (DNS) has proven itself an effective and robust tool in solving complex global stability problems of compressible flows. A Cayley transformation is required to add flexibility to our stability solver and to allow access to specific parts of the full global spectrum which would be out of reach without such a transformation. In order to robustify the overall global stability solver an efficient ILU-based preconditioner has been implemented. With this Cayley-transformed DNS-based Krylov method two flow cases were successfully investigated: (i) a compressible mixing layer, a rather simple but well-known problem, which served as a test case and (ii) a supersonic flow about a swept parabolic body, a challenging large-scale flow configuration.