Solution of MHD Flow with BEM Using Direct Radial Basis Function Interpolation

Abstract

In this study, the two-dimensional steady MHD Stokes and MHD incompressible flows of a viscous and electrically conducting fluid are considered in a lid-driven cavity under the impact of a uniform horizontal magnetic field. The MHD flow equations are solved iteratively in terms of velocity components, stream function, vorticity and pressure by using direct interpolation boundary element method (DIBEM) in which the inhomogeneity in the domain integral is interpolated by using radial basis functions. The boundary is discretized by constant elements and the sufficient number of the interior points are taken. The interpolation points are different from the source points due to the singularities of the fundamental solution. It is found that as Hartmann number increases, the main vortex of the flow shifts through the moving top lid with a decreasing magnitude and secondary flow below it is squeezed through the main flow leaving the rest of the cavity almost stagnant. The increase in M develops side layer near the moving lid, but weakens the effect of Re in the MHD incompressible flow.