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Analysis of incompressible massively separated viscous flows using unsteady Navier–Stokes equations
Author(s) -
Ghia K. N.,
Osswald G. A.,
Ghia U.
Publication year - 1989
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.1650090809
Subject(s) - stream function , curvilinear coordinates , mathematics , vorticity , navier–stokes equations , laminar flow , reynolds number , flow (mathematics) , computational fluid dynamics , hele shaw flow , mathematical analysis , geometry , open channel flow , vortex , compressibility , mechanics , physics , turbulence
The unsteady incompressible Navier–Stokes equations are formulated in terms of vorticity and stream‐function in generalized curvilinear orthogonal co‐ordinates to facilitate analysis of flow configurations with general geometries. The numerical method developed solves the conservative form of the vorticity transport equation using the alternating direction implicit method, whereas the streamfunction equation is solved by direct block Gaussian elimination. The method is applied to a model problem of flow over a backstep in a doubly infinite channel, using clustered conformal co‐ordinates. One‐dimensional stretching functions, dependent on the Reynolds number and the asymptotic behaviour of the flow, are used to provide suitable grid distribution in the separation and reattachment regions, as well as in the inflow and outflow regions. The optimum grid distribution selected attempts to honour the multiple length scales of the separated flow model problem. The asymptotic behaviour of the finite differenced transport equation near infinity is examined and the numerical method is carefully developed so as to lead to spatially second‐order‐accurate wiggle‐free solutions, i.e. with minimum dispersive error. Results have been obtained in the entire laminar range for the backstep channel and are in good agreement with the available experimental data for this flow problem, prior to the onset of three‐dimensionality in the experiment.