Transport processes associated with melting of an electrically conducting phase change material (PCM), placed inside a rectangular enclosure, under a low-gravity environment, and in the presence of a magnetic field, is simulated numerically. Electromagnetic forces damp the natural convection as well as the flow induced by sedimentation and/or floatation, and thereby simulate the low-gravity environment of outer space. Computational experiments are conducted for both side-wall healing and top-wall healing under a horizontal magnetic field, The governing equations are discretized using a control-volume-based finite difference scheme, Numerical solutions are obtained for a true low-gravity environment as well as for the simulated low-gravity conditions that are a result of the presence of a horizontal magnetic field. The effects of magnetic field on the natural convection, solid phase floatation/sedimentation, liquid/solid interface location, solid melting rate, and the flow patterns are investigated. It is found that the melting under a low-gravity environment reasonably can be simulated an earth via applying a strong horizontal magnetic field However, the flow patterns obtained for the true low-gravity environment are not similar to the corresponding cases solved for the simulated low gravity.