Computer Aided Analysis of Preconditioned Multistage Runge-Kutta Methods Applied to Solve the Compressible Reynolds Averaged Navier-Stokes Equations

The development of solution methods to approximate steady state solutions of the turbulent compressible Reynolds-averaged Navier-Stokes (RANS) equations is often based on several heuristics. In general a deep understanding of the power as well as the deficiencies of the methods is missing. It is the goal of this article to present an analysis tool which is applied to many well known solution techniques. The tool is based on Arnoldi's method to investigate approximations to the spectrum of the linearized equations. Numerical examples will demonstrate the good correlation between the approximate spectrum and the convergence behavior for the nonlinear equations.