A NEW ALGORITHM FOR SOLUTION OF EQUATIONS OF MHD CHANNEL FLOWS AT MODERATE HARTMANN NUMBERS

A new analytic finite element method (AFEM) is proposed for solving th e governing equations of steady magnetohydrodynamic (MHD) duct flows. By the AFEM code one is able to calculate the flow field, the induced magnetic field, and the first partial derivatives of these fields. The process of the code generation is rather lengthy and complicated, the refore, to save space, the actual formulation is presented only for re ctangular ducts. A distinguished feature of the AFEM code is the resol ving capability of the high gradients near the walls without use of lo cal mesh refinement. Results of traditional FEM, AFEM and finite diffe rence method (FDM) are compared with analytic results demonstrating th e manifest superiority of the AFEM code. The programs for the AFEM cod es are implemented in GAUSS using traditional computer arithmetic and work in the range of low and moderate Hartmann numbers M < 1000.