- Electromagnetic methods for controlling and optimization of melting process are applied both in the laboratory conditions and in industrial processes at least within past several decades. At that, usage of rotating and traveling magnetic fields was realized based on alternating or direct current electromagnetic facilities, or on permanent magnets systems. The last-named magnetic systems for such a task can make the driving equipment simpler and more efficient in certain applications. To examine the solid-liquid interface behavior and the possibility to control its dynamics while reducing melting process duration and temperature gradients, a three-dimensional numerical model was developed that accounted the temperature dependence of the metal properties and the presence of a mushy zone. Gallium melting process in an orthogonal container with heated and cooled side walls was numerically investigated under the impact of a traveling magnetic field from below. The mentioned field was created by the moving system of permanent magnets. The volumetric distribution of temperatures and the liquid-solid interface velocities were estimated for the cases with traveling magnetic field impact and with natural convection only. Numerical model was validated by comparison between the simulation of the flow in a rectangular container completely filled with liquid metal and experimental data obtained in low temperature Gallium-Indium-Tin alloy. Flow velocity components were measured by ultrasonic Doppler velocimeter. The results of the work allow extending the capabilities for a control of interface dynamics in liquid-solid metal systems, and in choosing of the optimal parameters of similar processes.