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The three‐dimensional prolonged adaptive unstructured finite element multigrid method for the Navier–Stokes equations
Author(s) -
Wille S. Ø.
Publication year - 1997
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(19970830)25:4<371::aid-fld553>3.0.co;2-t
Subject(s) - reynolds number , reynolds averaged navier–stokes equations , mathematics , multigrid method , finite element method , reynolds equation , pressure correction method , preconditioner , mathematical analysis , computational fluid dynamics , partial differential equation , linear system , physics , mechanics , turbulence , thermodynamics
This paper presents the development of the three‐ dimensional prolonged adaptive finite element equation solver for the Navier–Stokes equations. The finite element used is the tetrahedron with quadratic approximation of the velocities and linear approximation of the pressure. The equation system is formulated in the basic variables. The grid is adapted to the solution by the element Reynolds number. An element in the grid is refined when the Reynolds number of the element exceeds a preset limit. The global Reynolds number in the investigation is increased by scaling the solution for a lower Reynolds number. The grid is refined according to the scaled solution and the prolonged solution for the lower Reynolds number constitutes the start vector for the higher Reynolds number. Since the Reynolds number is the ratio of convection to diffusion, the grid refinements act as linearization and symmetrization of the equation system. The linear equation system of the Newton formulation is solved by CGSTAB with coupled node fill‐in preconditioner. The test problem considered is the three‐dimensional driven cavity flow. © 1997 John Wiley & Sons, Ltd.