Point and Line Implicit Methods to Improve the Efficiency and Robustness of the DLR Tau Code

Abstract

We present a line implicit preconditioned multistage Runge-Katta method to significantly improve the convergence rate for approximating steady state solutions of high Reynolds number viscous flows. The Runge-Katta method is used as a smoother in the context of an agglomarated multigrid method for unstructured grids. A simplification of a first order approximation to the Jacobian of the residual function is used as a preconditioner. Predetermined lines identifying mesh regions of high cell stretching are exploited to extract the relevant parts of the Jacobian matrix. The lines are identified using an efficient algorithm based on a weighted graph. This has the advantage that high aspect ratio cells are determined everywhere in the mesh, for example also in the wake of a wing.