Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/36382
標題: A Tailored Finite Point Method for Solving Steady MHD Duct Flow Problems with Boundary Layers
作者: Hsieh, P.W.
施因澤
Shih, Y.
Yang, S.Y.
關鍵字: Magnetohydrodynamic equations
Hartmann numbers
convection-dominated
problems
boundary layers
tailored finite point methods
finite
difference methods
element-method
期刊/報告no:: Communications in Computational Physics, Volume 10, Issue 1, Page(s) 161-182.
摘要: In this paper we propose a development of the finite difference method, called the tailored finite point method, for solving steady magnetohydrodynamic (MHD) duct flow problems with a high Hartmann number. When the Hartmann number is large, the MHD duct flow is convection-dominated and thus its solution may exhibit localized phenomena such as the boundary layer. Most conventional numerical methods can not efficiently solve the layer problem because they are lacking in either stability or accuracy. However, the proposed tailored finite point method is capable of resolving high gradients near the layer regions without refining the mesh. Firstly, we devise the tailored finite point method for the scalar inhomogeneous convection-diffusion problem, and then extend it to the MHD duct flow which consists of a coupled system of convection-diffusion equations. For each interior grid point of a given rectangular mesh, we construct a finite-point difference operator at that point with some nearby grid points, where the coefficients of the difference operator are tailored to some particular properties of the problem. Numerical examples are provided to show the high performance of the proposed method.
URI: http://hdl.handle.net/11455/36382
ISSN: 1815-2406
文章連結: http://dx.doi.org/10.4208/cicp.070110.020710a
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