An exponential compact difference scheme for solving 2D steady magnetohydrodynamic (MHD) duct flow problems

Authors:
Yan Li;Zhen F. Tian
Affiliations:
Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433, PR China and School of Metallurgy and Materials, University of Birmingham, Birmingham, Edgbaston B15 2TT, UK;Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433, PR China
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

In this article, an exponential high-order compact (EHOC) difference scheme on the nine-point stencil is developed for the solution of the coupled equations representing the steady incompressible, viscous magnetohydrodynamic (MHD) flow through a straight channel of rectangular section. A key property of the EHOC scheme is that it has excellent stability and higher accuracy so that the high gradients near the boundary layer areas can be effectively resolved without refining the mesh. Numerical experiments are carried out to validate the performance of the currently proposed scheme. Computation results of the MHD flow in the 2D square-channel problems with different wall conductivities are presented for Hartmann numbers ranging from 10 to 10^6. The numerical solutions obtained with the newly developed EHOC scheme are also compared with analytic solutions and numerical results by other available methods in the literature.