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Uniformly convergent scheme for steady MHD duct flow problems with high Hartmann numbers on structured and unstructured grids

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  • Sun, Tao
  • Wang, Yihong

Abstract

The steady incompressible Magnetohydrodynamic (MHD) duct flow problems with a transverse magnetic field at high Hartmann numbers (Ha) is a coupled system of convection-dominated diffusion equations and the solutions contain sharp boundary layers. We develop a five-point scheme and an edge-centered scheme on structured and unstructured grids with tailored finite point method (TFPM) for solving the coupled system of convection–diffusion equations. The five-point scheme is an upwind difference scheme, where the coefficients of the difference operator are tailored to some particular properties of the convection–diffusion equation with constant coefficients on the local cell. The edge-centered scheme is constructed by the continuity of the normal fluxes for each edge. The normal flux is expressed in terms of the edge-centered unknowns defined at the local cell and the unknowns at the adjacent cells are not needed. Uniform second order convergence can be obtained by the edge-centered scheme on structured and unstructured grids over a wide range of Ha 10 to 106. Both of the two schemes can correctly reproduce the fast change of the solutions which contain sharp boundary layers at high Ha even without refining the mesh. Numerical examples are provided to show the accuracy and of the TFPM.

Suggested Citation

  • Sun, Tao & Wang, Yihong, 2023. "Uniformly convergent scheme for steady MHD duct flow problems with high Hartmann numbers on structured and unstructured grids," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 336-359.
    • Handle: RePEc:eee:matcom:v:212:y:2023:i:c:p:336-359
    DOI: 10.1016/j.matcom.2023.05.007
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