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A Hermite finite element method for incompressible fluid flow
Author(s) -
Holdeman J. T.
Publication year - 2009
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.2154
Subject(s) - stream function , pointwise , divergence (linguistics) , mathematics , finite element method , flow (mathematics) , hermite polynomials , incompressible flow , compressibility , pressure correction method , function (biology) , computation , mathematical analysis , flow velocity , velocity potential , geometry , physics , mechanics , vorticity , vortex , algorithm , linguistics , philosophy , evolutionary biology , biology , thermodynamics , boundary value problem
We describe some Hermite stream function and velocity finite elements and a divergence‐free finite element method for the computation of incompressible flow. Divergence‐free velocity bases defined on (but not limited to) rectangles are presented, which produce pointwise divergence‐free flow fields (∇· u h ≡0). The discrete velocity satisfies a flow equation that does not involve pressure. The pressure can be recovered as a function of the velocity if needed. The method is formulated in primitive variables and applied to the stationary lid‐driven cavity and backward‐facing step test problems. Copyright © 2009 John Wiley & Sons, Ltd.