In previous work [Lucas, P.,Bijl, H., and Zuijlen, A.H. van(2010)], we have shown that a Jacobian-free Newton-Krylov (JFNK) algorithm, preconditioned with an approximate factorization of the Jacobian which approximately matches the target residual operator, enables a speed up of a factor of 10 compared to nonlinear multigrid (NMG) for two-dimensional, large Reynolds number, unsteady flow computations. Furthermore, in [Lucas, P., Zuijlen, A.H. van, and Bijl, H. (2010)] we show that this algorithm also greatly outperforms NMG for parameter studies into the maximum aspect ratio, grid density and physical time step: speeds ups, up to a factor of 25 are achieved.

The goal of this paper is to demonstrate the wider applicability of the preconditioned JFNK algorithm by studying incompressible flow and an incompressible fluid structure-interaction (FSI) case. It is shown that the preconditioned JFNK algorithm is able to tackle the stiffness induced by the low Mach regime, making it possible to apply a compressible flow solver to nearly incompressible flow. Furthermore, it is shown that the preconditioned JFNK algorithm can be readily applied to FSI problems.}, DOI = {10.3970/cmes.2010.059.079} }