@Article{cmes.2010.059.079,
AUTHOR = {Peter  Lucas,  Alexander H. van  Zuijlen, Hester  Bijl},
TITLE = {A Preconditioned JFNK Algorithm Applied to Unsteady Incompressible Flow and Fluid Structure Interaction Problems},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {59},
YEAR = {2010},
NUMBER = {1},
PAGES = {79--106},
URL = {http://www.techscience.com/CMES/v59n1/25497},
ISSN = {1526-1506},
ABSTRACT = {Despite the advances in computer power and numerical algorithms over the last decades, solutions to unsteady flow problems remain computing time intensive.<br/>
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.<br/>
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}
}