Comparison of FSM and BEM Solutions of MHD Equations

We consider the numerical solutions of the MagnetoHydroDynamic (MHD) equations both in 2D and 3D domains using Fundamental Solution Method (FSM) also known as meshless method and Boundary Element Method (BEM) where both of them uses the fundamental solution of the differential operator. The considered MHD equations are transformed to the convection-diffusion type and modified Helmholtz type forms in order to apply the considered numerical methods. Formulized four different types of numerical schemes are compared with the either the exact solution if possible or with the Finite Element Method (FEM) results for the different Hartmann number values. Obtained solutions are displayed in terms of tables and visualized with figures of the contour plots.