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A least‐squares finite element method for incompressible Navier‐Stokes problems
Author(s) -
Jiang BoNan
Publication year - 1992
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.1650140706
Subject(s) - mathematics , reynolds number , finite element method , incompressible flow , pressure correction method , saddle point , navier–stokes equations , mathematical analysis , compressibility , least squares function approximation , mixed finite element method , flow (mathematics) , geometry , mechanics , physics , turbulence , statistics , estimator , thermodynamics
A least‐squares finite element method based on the velocity–pressure–vorticity formulation was proposed for solving steady incompressible Navier‐Stokes problems. This method leads to a minimization problem rather than to the saddle point problem of the classic mixed method and can thus accommodate equal‐order interpolations. The method has no parameter to tune. The associated algebraic system is symmetric and positive definite. In order to show the validity of the method for high‐Reynolds‐number problems, this paper provides numerical results for cavity flow at Reynolds number up to 10 000 and backward‐facing step flow at Reynolds number up to 900.