Upwinding Meshfree Point Collocation Method for Unsteady Magnetohydrodynamic Flow 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 the velocity field for the unsteady magnetohydrodynamic (MHD) flow through a straight duct of rectangular section with insulated walls. Computations have been carried out for the unsteady MHD flow, which is under the external applied magnetic field of arbitrary orientation, of different Hartmann number from 5 to 106 and at various time levels. As the adaptive upwinding local support domain is introduced in the meshless collocation method, numerical results show that the method can compute MHD problems with Hartmann numbers up to 106 with good accuracy. The results also show that as Hartmann number increases, the time needed to reach the steady state decreases.