On nonlinear preconditioners in Newton–Krylov methods for unsteady flows
Philipp Birken, Antony Jameson · International Journal for Numerical Methods in Fluids · 2009
Abstract The application of nonlinear schemes like dual time stepping as preconditioners in matrix‐free Newton–Krylov‐solvers is considered and analyzed, with a special emphasis on unsteady viscous flows. 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 is demonstrated through numerical results. Copyright © 2009 John Wiley & Sons, Ltd.