Two-level finite element method with a stabilizing subgrid for the incompressible MHD equations


AYDIN BAYRAM S. , Nesliturk A. I. , Tezer-Sezgin M.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, cilt.62, ss.188-210, 2010 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 62 Konu: 2
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1002/fld.2019
  • Dergi Adı: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
  • Sayfa Sayısı: ss.188-210

Özet

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 (C) 2009 John Wiley & Sons, Ltd.