Verfahren zur Beschleunigung der Lösung der Euler- und Navier-Stokes-Gleichungen bei stationären Über- und Hyperschallströmungen

Kurzfassung

Two new acceleration methods for explicit multistage time- stepping schemes have been developed. Within the first method, the residuals of the discretized Euler or of the Navier-Stokes equations are smoothed using an upwind-biased operator. This permits an increased time step leading to faster convergence behaviour to the steady-state. The goal of the second method is to improve the convergence behaviour of multigrid schemes for supersonic and hypersonic flows. This is accomplished by employing an upwind-weighted operator for the interpolation of the coarse-grid solution corrections to the fine grid, instead of the usual central weighted one. It proves to be beneficial to determine the upwind direction using the local Mach number, which is calculated with the contravariant velocity. The stability and damping properties of both methods are investigated by applying von Neumann analysis to different one-.