TY - JOUR
T1 - A Tailored Finite Point Method for Solving Steady MHD Duct Flow Problems with Boundary Layers
AU - Po-Wen Hsieh, Yintzer Shih & Suh-Yuh Yang
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 - <p style="text-align: justify;">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.</p>