Abstract
The meshless point collocation method (MPC) is used for magnetohydrodynamics (MHD) flow problems in channels with insulating walls having rectangular, circular or elliptical cross sections. The MPC method is a truly meshless method and computationally efficient. The maximum principle for the discrete harmonic operator in the meshless point collocation method has been proven recently, and the convergence proof for the numerical solution of the Poisson problem with Dirichlet boundary conditions have been attained, accordingly. The basis functions are constructed using the Moving Least Squares (MLS) approximation. Furthermore, our computations are compared with available numerical results, and analytical solutions, as well, and the superiority of MPC method is demonstrated. We present results for Hartmann number up to 1000.
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