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Two‐level finite element method with a stabilizing subgrid for the incompressible MHD equations
Author(s) -
Aydın S. H.,
Nesliturk A. I.,
TezerSezgin M.
Publication year - 2009
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.2019
Subject(s) - finite element method , discretization , magnetohydrodynamics , mathematics , magnetohydrodynamic drive , piecewise linear function , galerkin method , incompressible flow , discontinuous galerkin method , flow (mathematics) , piecewise , mathematical analysis , physics , geometry , magnetic field , quantum mechanics , thermodynamics
We consider the Galerkin finite element method (FEM) for the incompressible magnetohydrodynamic (MHD) equations in two dimension. The domain is discretized into a set of regular triangular elements and the finite‐dimensional spaces employed consist of piecewise continuous linear interpolants enriched with the residual‐free bubble functions. To find the bubble part of the solution, a two‐level FEM with a stabilizing subgrid of a single node is described and its application to the MHD equations is displayed. Numerical approximations employing the proposed algorithm are presented for three benchmark problems including the MHD cavity flow and the MHD flow over a step. The results show that the proper choice of the subgrid node is crucial to get stable and accurate numerical approximations consistent with the physical configuration of the problem at a cheap computational cost. Furthermore, the approximate solutions obtained show the well‐known characteristics of the MHD flow. Copyright © 2009 John Wiley & Sons, Ltd.
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