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An exponential compact difference scheme for solving 2D steady magnetohydrodynamic (MHD) duct flow problems. (English) Zbl 1431.76096
Summary: 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 on 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 obtained by other available methods in the literature.

##### MSC:
 76M20 Finite difference methods applied to problems in fluid mechanics 76W05 Magnetohydrodynamics and electrohydrodynamics
##### Keywords:
boundary layers; mesh refinement; square-channel flow
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