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A least‐squares finite element method for time‐dependent incompressible flows with thermal convection
Author(s) -
Tang Li Q.,
Tsang Tate T. H.
Publication year - 1993
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.1650170402
Subject(s) - finite element method , compressibility , mechanics , pressure correction method , moving least squares , mathematics , incompressible flow , convection , least squares function approximation , computational fluid dynamics , thermal , physics , mathematical analysis , classical mechanics , thermodynamics , statistics , estimator
The time‐dependent Navier–Stokes equations and the energy balance equation for an incompressible, constant property fluid in the Boussinesq approximation are solved by a least‐squares finite element method based on a velocity–pressure–vorticity–temperature–heat‐flux ( u – P –ω– T – q ) formulation discretized by backward finite differencing in time. The discretization scheme leads to the minimization of the residual in the l 2 ‐norm for each time step. Isoparametric bilinear quadrilateral elements and reduced integration are employed. Three examples, thermally driven cavity flow at Rayleigh numbers up to 10 6 , lid‐driven cavity flow at Reynolds numbers up to 10 4 and flow over a square obstacle at Reynolds number 200, are presented to validate the method.