The averaged quasi-steady flow patterns of metal melt situated in alternating magnetic field are studied numerically. It is taken into account the buoyancy due to non-uniform heating, the intensive radiation heatsink from the melt surface and the Lorentz forces arising in conductor in the alternating magnetic field. The governing equations of the suggested mathematical model are given and the model validations are described. The flow regime maps are plotted based on analysis of melt velocity dependence on the Hartmann number and the parameter of magnetic field diffusion. Flow patterns corresponding each parameter area at the map are given and interpreted. The way of acceleration of melt motion computation is suggested. (C) 2018 Published by Elsevier Ltd.