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Fourth‐order compact formulation of Navier–Stokes equations and driven cavity flow at high Reynolds numbers
Author(s) -
Erturk E.,
Gökçöl C.
Publication year - 2005
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.1061
Subject(s) - navier–stokes equations , mathematics , reynolds number , pressure correction method , tridiagonal matrix , reynolds averaged navier–stokes equations , compressibility , flow (mathematics) , incompressible flow , mathematical analysis , non dimensionalization and scaling of the navier–stokes equations , computational fluid dynamics , geometry , mechanics , physics , turbulence , eigenvalues and eigenvectors , quantum mechanics
A new fourth‐order compact formulation for the steady 2‐D incompressible Navier–Stokes equations is presented. The formulation is in the same form of the Navier–Stokes equations such that any numerical method that solve the Navier–Stokes equations can easily be applied to this fourth‐order compact formulation. In particular, in this work the formulation is solved with an efficient numerical method that requires the solution of tridiagonal systems using a fine grid mesh of 601 × 601. Using this formulation, the steady 2‐D incompressible flow in a driven cavity is solved up to Reynolds number with Re = 20 000 fourth‐order spatial accuracy. Detailed solutions are presented. Copyright © 2005 John Wiley & Sons, Ltd.