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Petrov‐Galerkin methods on multiply connected domains for the vorticity‐stream function formulation of the incompressible Navier‐Stokes equations
Author(s) -
Tezduyar T. E.,
Glowinski R.,
Liou J.
Publication year - 1988
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.1650081012
Subject(s) - stream function , vorticity , navier–stokes equations , vorticity equation , mathematics , mathematical analysis , compressibility , pressure correction method , boundary value problem , galerkin method , computational fluid dynamics , finite element method , vortex , physics , mechanics , thermodynamics
In this paper we present streamline‐upwind/Petrov‐Galerkin finite element procedures for two‐dimensional fluid dynamics computations based on the vorticity‐stream function formulation of the incompressible Navier‐Stokes equations. We address the difficulties associated with the convection term in the vorticity transport equation, lack of boundary condition for the vorticity at no‐slip boundaries, and determination of the value of the stream function at the internal boundaries for multiply connected domains. The proposed techniques, implemented within the framework of block‐iteration methods, have successfully been applied to various problems involving simply and multiply connected domains.