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

Peter Lucas1, Alexander H. van Zuijlen1, Hester Bijl1
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.

Keywords

Jacobian-free Newton-Krylov, low Mach number, unsteady flow, fluid-structure interaction.

Cite This Article

Lucas, P., H., A., Bijl, H. (2010). A Preconditioned JFNK Algorithm Applied to Unsteady Incompressible Flow and Fluid Structure Interaction Problems. CMES-Computer Modeling in Engineering & Sciences, 59(1), 79–106.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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