Premium
Numerical solution of the incompressible Navier–Stokes equations with an upwind compact difference scheme
Author(s) -
Yanwen Ma,
Dexun Fu,
Kobayashi T.,
Taniguchi N.
Publication year - 1999
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/(sici)1097-0363(19990715)30:5<509::aid-fld851>3.0.co;2-e
Subject(s) - discretization , upwind scheme , mathematics , navier–stokes equations , pressure correction method , compact finite difference , poisson's equation , finite difference , mathematical analysis , finite difference method , compressibility , computational fluid dynamics , central differencing scheme , finite element method , finite difference coefficient , physics , mechanics , mixed finite element method , thermodynamics
A new finite difference method for the discretization of the incompressible Navier–Stokes equations is presented. The scheme is constructed on a staggered‐mesh grid system. The convection terms are discretized with a fifth‐order‐accurate upwind compact difference approximation, the viscous terms are discretized with a sixth‐order symmetrical compact difference approximation, the continuity equation and the pressure gradient in the momentum equations are discretized with a fourth‐order difference approximation on a cell‐centered mesh. Time advancement uses a three‐stage Runge–Kutta method. The Poisson equation for computing the pressure is solved with preconditioning. Accuracy analysis shows that the new method has high resolving efficiency. Validation of the method by computation of Taylor's vortex array is presented. Copyright © 1999 John Wiley & Sons, Ltd.