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SIMPLE‐type preconditioners for cell‐centered, colocated finite volume discretization of incompressible Reynolds‐averaged Navier–Stokes equations
Author(s) -
Klaij C. M.,
Vuik C.
Publication year - 2012
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3686
Subject(s) - preconditioner , reynolds averaged navier–stokes equations , solver , finite volume method , discretization , stencil , reynolds number , mathematics , navier–stokes equations , multigrid method , unstructured grid , iterative method , compressibility , mathematical analysis , computational fluid dynamics , mathematical optimization , grid , turbulence , geometry , mechanics , physics , computational science , partial differential equation
SUMMARY This paper contains a comparison of four SIMPLE‐type methods used as solver and as preconditioner for the iterative solution of the (Reynolds‐averaged) Navier–Stokes equations, discretized with a finite volume method for cell‐centered, colocated variables on unstructured grids. A matrix‐free implementation is presented, and special attention is given to the treatment of the stabilization matrix to maintain a compact stencil suitable for unstructured grids. We find SIMPLER preconditioning to be robust and efficient for academic test cases and industrial test cases. Compared with the classical SIMPLE solver, SIMPLER preconditioning reduces the number of nonlinear iterations by a factor 5–20 and the CPU time by a factor 2–5 depending on the case. The flow around a ship hull at Reynolds number 2E9, for example, on a grid with cell aspect ratio up to 1:1E6, can be computed in 3 instead of 15 h.Copyright © 2012 John Wiley & Sons, Ltd.