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A high‐order finite difference method for incompressible fluid turbulence simulations
Author(s) -
Vedy Eric,
Viazzo Stephane,
Schiestel Roland
Publication year - 2003
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.516
Subject(s) - turbulence , compressibility , pressure correction method , mathematics , incompressible flow , hermitian matrix , navier–stokes equations , fourier transform , spectral method , poisson's equation , computational fluid dynamics , flow (mathematics) , mathematical analysis , physics , mechanics , geometry , pure mathematics
A Hermitian–Fourier numerical method for solving the Navier–Stokes equations with one non‐homogeneous direction had been presented by Schiestel and Viazzo ( Internat. J. Comput. Fluids 1995; 24 (6):739). In the present paper, an extension of the method is devised for solving problems with two non‐homogeneous directions. This extension is indeed not trivial since new algorithms will be necessary, in particular for pressure calculation. The method uses Hermitian finite differences in the non‐periodic directions whereas Fourier pseudo‐spectral developments are used in the remaining periodic direction. Pressure–velocity coupling is solved by a simplified Poisson equation for the pressure correction using direct method of solution that preserves Hermitian accuracy for pressure. The turbulent flow after a backward facing step has been used as a test case to show the capabilities of the method. The applications in view are mainly concerning the numerical simulation of turbulent and transitional flows. Copyright © 2003 John Wiley & Sons, Ltd.