A Preconditioned JFNK Algorithm Applied to Unsteady Incompressible Flow and Fluid Structure Interaction Problems
Peter Lucas; and Alexander H. van Zuijlen and Hester Bijl

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 59, No. 1, pp. 79-106, 2010
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Keywords Jacobian-free Newton-Krylov, low Mach number, unsteady flow, fluid-structure interaction.
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 [ ` 12 `
12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Lucas_EfficientUnsteady], 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 [ ` 12 `
12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Lucas_FastUnsteady] 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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