Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 228, Issue 17, Pages 6316-6332Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2009.05.019
Keywords
Navier-Stokes equations; Fractional methods; Stabilized finite element; Predictor-corrector scheme; Incremental projection scheme; Parallel implementation; High performance computing
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This paper presents a parallel implementation of fractional solvers for the incompressible Navier-Stokes equations using an algebraic approach. Under this framework, predictor-corrector and incremental projection schemes are seen as sub-classes of the same class, making apparent its differences and similarities. An additional advantage of this approach is to set a common basis for a parallelization strategy, which can be extended to other split techniques or to compressible flows. The predictor-corrector scheme consists in solving the momentum equation and a modified continuity equation (namely a simple iteration for the pressure Schur complement) consecutively in order to converge to the monolithic solution, thus avoiding fractional errors. On the other hand, the incremental projection scheme solves only one iteration of the predictor-corrector per time step and adds a correction equation to fulfill the mass conservation. As shown in the paper, these two schemes are very well suited for massively parallel implementation. In fact, when compared with monolithic schemes, simpler solvers and preconditioners can be used to solve the non-symmetric momentum equations (GMRES, Bi-CGSTAB) and to solve the symmetric continuity equation (CC, Deflated CC). This gives good speedup properties of the algorithm. The implementation of the mesh partitioning technique is presented, as well as the parallel performances and speedups for thousands of processors. (C) 2009 Elsevier Inc. All rights reserved.
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