A two-dimensional mathematical model was built to describe the melting process of cylindrical basalt particle bed in a crucible. The melting processes with respect to the factors of thermal boundary conditions and particle sizes of basalt were simulated by using the numerical method (FDM). The governing equations were discretized in tridiagonal matrix form and were solved by using the tridiagonal matrix algorithm (TDMA) as well as the alternative direction implicit (ADI) solver. The temperature distribution, the moving law of the two dimensional phase-change boundaries, the thermal current distribution were given through the numerical simulation. The results provided a theoretical basis for deciding heating procedure, for evaluating power import and controlling furnace temperature and for predicting basalt melting states etc. In the experiment, an electrical furnace was designed based on the computations. It has been proved that the simulation results are reasonably coincident with the experimental data. A two-dimensional mathematical model was built to describe the melting process of cylindrical basalt particle bed in a crucible. The melting processes with respect to the factors of thermal boundary conditions and particle sizes of basalt were simulated by using the numerical method (FDM). The governing equations were discretized in tridiagonal matrix form and was solved by using the tridiagonal matrix algorithm (TDMA) as well as the alternative direction implicit (ADI) solver. The temperature distribution, the moving law of the two-dimensional phase-change boundaries, the thermal current distribution were given through the numerical simulation. The results provide a theoretical basis for deciding heating procedure, for evaluating power import and controlling furnace temperature and for predicting basalt melting states etc. In the experiment, an electrical furnace was designed based on the computations It has been proved that the simulation results are reasonably coincident with the experimental data.