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A NON–LINEAR ADAPTED TRI–TREE MULTIGRID SOLVER FOR FINITE ELEMENT FORMULATION OF THE NAVIER–STOKES EQUATIONS
Author(s) -
WILLE S. Ø.
Publication year - 1996
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(19960615)22:11<1041::aid-fld386>3.0.co;2-k
Subject(s) - multigrid method , solver , finite element method , mathematics , iterative method , grid , navier–stokes equations , iterated function , mathematical optimization , partial differential equation , mathematical analysis , geometry , physics , compressibility , thermodynamics
An iterative adaptive equation multigrid solver for solving the implicit Navier–Stokes equations simultaneously with tri‐tree grid generation is developed. The tri‐tree grid generator builds a hierarchical grid structur e which is mapped to a finite element grid at each hierarchical level. For each hierarchical finite element multigrid the Navier–Stokes equations are solved approximately. The solution at each level is projected onto the next finer grid and used as a start vector for the iterative equation solver at the finer level. When the finest grid is reached, the equation solver is iterated until a tolerated solution is reached. The iterative multigrid equation solver is preconditioned by incomplete LU factorization with coupled node fill‐in. The non‐linear Navier–Stokes equations are linearized by both the Newton method and grid adaption. The efficiency and behaviour of the present adaptive method are compared with those of the previously developed iterative equation solver which is preconditioned by incomplete LU factorization with coupled node fill‐in.