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Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow
Author(s) -
Lavery N.,
Taylor C.
Publication year - 1999
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/(sici)1097-0363(19990730)30:6<609::aid-fld733>3.0.co;2-6
Subject(s) - multigrid method , conjugate gradient method , mathematics , pressure correction method , finite element method , biconjugate gradient stabilized method , biconjugate gradient method , discretization , incompressible flow , mathematical analysis , compressibility , flow (mathematics) , conjugate residual method , geometry , mathematical optimization , partial differential equation , mechanics , physics , computer science , thermodynamics , gradient descent , machine learning , artificial neural network
Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time‐independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi–Babuska condition. The k – l model is used to complete the turbulence closure problem. The non‐symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a ‘V‐cycling’ schedule. These methods are all compared to the non‐symmetric frontal solver. Copyright © 1999 John Wiley & Sons, Ltd.