Preconditioned Newton methods to approximate solutions of the Reynolds averaged Navier-Stokes equations

Abstract

We consider nonlinear agglomeration multigrid methods tailored to the efficient and robust solution of boundary value problems corresponding to the Reynolds averaged Navier-Stokes equations for the simulation of high Reynolds number turbulent flows. The presented solution algorithms are based on nonlinear agglomeration multigrid methods including implicit Runge-Kutta smoothers. The final formulation of these methods allows to interpret these smoothers as kinds of stabilized preconditioned Newton methods. The application of simplifications is used to derive almost all solution methods well known in the world of computational fluid dynamics. This hierarchy of methods gives insight in the potential and shortcomings of several established methods. To get a deeper understanding of the methods an analysis tool is suggested to evaluate certain smoothers. Several examples are presented to show the potential and shortcomings of certain methods derived in this thesis. Comparisons are done with respect to both robustness and efficiency of the scheme.