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A compact finite difference method on staggered grid for Navier–Stokes flows
Author(s) -
Zhang K. K. Q.,
Shotorban B.,
Minkowycz W. J.,
Mashayek F.
Publication year - 2006
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.1207
Subject(s) - compact finite difference , grid , finite volume method , turbulence , compressibility , mathematics , large eddy simulation , finite difference method , flow (mathematics) , finite difference , mathematical analysis , boundary value problem , navier–stokes equations , periodic boundary conditions , boundary (topology) , mechanics , geometry , physics
Compact finite difference methods feature high‐order accuracy with smaller stencils and easier application of boundary conditions, and have been employed as an alternative to spectral methods in direct numerical simulation and large eddy simulation of turbulence. The underpinning idea of the method is to cancel lower‐order errors by treating spatial Taylor expansions implicitly. Recently, some attention has been paid to conservative compact finite volume methods on staggered grid, but there is a concern about the order of accuracy after replacing cell surface integrals by average values calculated at centres of cell surfaces. Here we introduce a high‐order compact finite difference method on staggered grid, without taking integration by parts. The method is implemented and assessed for an incompressible shear‐driven cavity flow at Re = 10 3 , a temporally periodic flow at Re = 10 4 , and a spatially periodic flow at Re = 10 4 . The results demonstrate the success of the method. Copyright © 2006 John Wiley & Sons, Ltd.