Volume 10, Issue 1
A Tailored Finite Point Method for Solving Steady MHD Duct Flow Problems with Boundary Layers

Po-Wen Hsieh, Yintzer Shih & Suh-Yuh Yang

Commun. Comput. Phys., 10 (2011), pp. 161-182.

Published online: 2011-10

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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.

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@Article{CiCP-10-161, author = {}, title = {A Tailored Finite Point Method for Solving Steady MHD Duct Flow Problems with Boundary Layers}, journal = {Communications in Computational Physics}, year = {2011}, volume = {10}, number = {1}, pages = {161--182}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.070110.020710a}, url = {http://global-sci.org/intro/article_detail/cicp/7439.html} }
TY - JOUR T1 - A Tailored Finite Point Method for Solving Steady MHD Duct Flow Problems with Boundary Layers JO - Communications in Computational Physics VL - 1 SP - 161 EP - 182 PY - 2011 DA - 2011/10 SN - 10 DO - http://doi.org/10.4208/cicp.070110.020710a UR - https://global-sci.org/intro/article_detail/cicp/7439.html KW - AB -

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.

Po-Wen Hsieh, Yintzer Shih & Suh-Yuh Yang. (2020). A Tailored Finite Point Method for Solving Steady MHD Duct Flow Problems with Boundary Layers. Communications in Computational Physics. 10 (1). 161-182. doi:10.4208/cicp.070110.020710a
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