A compressible MHD (magnetohydrodynamic) model composed of MHD N-S (navier-stokes) equations and magnetic induction equations was proposed for analyzing the magnetohydrodynamic characteristics in MHD generator and MHD accelerator channels of MPC (magneto-plasma-chemical) propulsion system. A splitting algorithm based on an alternative iteration was developed for solving the two sets of equations. As a test case, a supersonic MHD flow in a square duct was simulated. The numerical results were compared with the results computed by solving the classical N-S equations for the perfect gas flow, together with the results computed utilizing the degenerate MHD N-S equations for the same channel flow with constant applied magnetic field. The thermo-electro-magnetic performances of the test cases with constant and variable applied fields were then discussed.