NUMERICAL SOLUTION OF MAGNETOHYDRODYNAMIC FLOW PROBLEM USING RADIAL BASIS FUNCTION BASED FINITE DIFFERENCE METHOD

Abstract

This paper focuses on the application of Radial Basis Function generated Finite Difference Method (RBF-FD) to solve Magnetohydrodynamic (MHD) flow equation in a rectangular duct in the presence of the transverse external oblique magnetic field. Multiquadric (MQ) Radial Basis Function is used to obtain the numerical solution of the MHD flow problem. Accuracy of the solution can be improved by varying the shape parameter in MQ function. The solution obtained from RBF-FD method is compared with the analytical solution and classical Finite Difference solution. Contours are presented for various Hartmann numbers with different grid sizes and directions of the applied magnetic field. The behaviour of velocity and the magnetic field of the MHD flow have been studied using the contours.