Upwinding meshfree point collocation method for steady MHD flow with arbitrary orientation of applied magnetic field at high Hartmann numbers

In this paper, a meshfree point collocation method, with an upwinding scheme, is presented to obtain the numerical solutions of the coupled equations in velocity and magnetic field for the fully developed magnetohydrodynamic (MHD) flow through an insulated straight duct of rectangular section. The moving least-square (MLS) approximation is employed to construct the shape functions in conjunction with the framework of the point collocation method. Computations have been carried out for different applied magnetic field orientations and a wide range of values of Hartmann number from 5 to 10⁶. As the adaptive upwinding local support domain is introduced in the meshless point collocation method, numerical results show that the method may compute MHD problems not only at low and moderate values but also at high values of the Hartmann number with high accuracy and good convergence.