Melt flow phenomena of magnetic Czochralski processes are simulated numerically. A model is established for the system that can grow a 5 inch diameter single crystal from the melt in a 14 inch diameter cylindrical crucible. Effective conditions to suppress convection adequately are studied by varying rotation rates of the crucible and the crystal for given magnetic fields. When the axial magnetic force is used, the method of co-rotation of the crystal and the crucible is found more effective to suppress meridional circulation that the conventional counter-rotation operation.