Open Access

ARTICLE

A Preconditioned JFNK Algorithm Applied to Unsteady Incompressible Flow and Fluid Structure Interaction Problems

Peter Lucas¹, Alexander H. van Zuijlen¹, Hester Bijl¹

1 Faculty of Aerospace Engineering, Delft University of Technology, P.O. Box 5058, 2600 GB Delft, The Netherlands

Computer Modeling in Engineering & Sciences 2010, 59(1), 79-106. https://doi.org/10.3970/cmes.2010.059.079

Abstract

Despite the advances in computer power and numerical algorithms over the last decades, solutions to unsteady flow problems remain computing time intensive.
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.

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