A bubble-stabilized least-squares finite element method for steady MHD duct flow problems at high Hartmann numbers

Po Wen Hsieh, Suh Yuh Yang

研究成果: 雜誌貢獻期刊論文同行評審

18 引文 斯高帕斯(Scopus)

摘要

In this paper we devise a stabilized least-squares finite element method using the residual-free bubbles for solving the governing equations of steady magnetohydrodynamic duct flow. We convert the original system of second-order partial differential equations into a first-order system formulation by introducing two additional variables. Then the least-squares finite element method using C0 linear elements enriched with the residual-free bubble functions for all unknowns is applied to obtain approximations to the first-order system. The most advantageous features of this approach are that the resulting linear system is symmetric and positive definite, and it is capable of resolving high gradients near the layer regions without refining the mesh. Thus, this approach is possible to obtain approximations consistent with the physical configuration of the problem even for high values of the Hartmann number. Before incoorperating the bubble functions into the global problem, we apply the Galerkin least-squares method to approximate the bubble functions that are exact solutions of the corresponding local problems on elements. Therefore, we indeed introduce a two-level finite element method consisting of a mesh for discretization and a submesh for approximating the computations of the residual-free bubble functions. Numerical results confirming theoretical findings are presented for several examples including the Shercliff problem.

原文???core.languages.en_GB???
頁(從 - 到)8301-8320
頁數20
期刊Journal of Computational Physics
228
發行號22
DOIs
出版狀態已出版 - 1 12月 2009

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