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A Tailored Finite Point Method for Solving Steady MHD Duct Flow Problems with Boundary Layers

Published online by Cambridge University Press:  20 August 2015

Po-Wen Hsieh ,
Yintzer Shih  and
Suh-Yuh Yang
Po-Wen Hsieh*
Affiliation:
Department of Mathematics, National Central University, Jhongli City, Taoyuan County 32001, Taiwan
Yintzer Shih*
Affiliation:
Department of Applied Mathematics, National Chung Hsing University, Taichung 40227, Taiwan
Suh-Yuh Yang*
Affiliation:
Department of Mathematics, National Central University, Jhongli City, Taoyuan County 32001, Taiwan
*
Email:952401001@cc.ncu.edu.tw
Email:yintzer_shih@email.nchu.edu.tw
Corresponding author.Email:syyang@math.ncu.edu.tw
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Abstract

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.

Keywords

65N0665N1276W05Magnetohydrodynamic equationsHartmann numbersconvection-dominated problemsboundary layerstailored finite point methodsfinite difference methods
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 1 , July 2011 , pp. 161 - 182
Copyright
Copyright © Global Science Press Limited 2011

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