On Nonlinear Preconditioners in Newton-Krylov-Methods for Unsteady Flows

The application of nonlinear schemes like dual time stepping as preconditioners in matrix-free Newton-Krylov-solvers is considered and analyzed. We provide a novel formulation of the left preconditioned operator that says it is in fact linear in the matrix-free sense, but changes the Newton scheme. This allows to get some insight in the convergence properties of these schemes which are demonstrated through numerical results.

Preconditioner updates applied to CFD model problems

In the present paper we concentrate on solving sequences of nonsymmetric linear systems with block structure arising from compressible flow problems. We attempt to improve the solution process by sharing part of the computational effort throughout the sequence. This is achieved by application of a cheap updating technique for preconditioners which we adapted in order to be used for our applications. Tested on three benchmark compressible flow problems, the strategy speeds up the entire computation with an acceleration being particularly pronounced in phases of instationary behavior.