The cold crucible vitrification technique is one of the most promising techniques to vitrify the nuclear waste. However, the low temperature near the bottom of the crucible will increase the viscosity and thus decrease the fluidity of the glass melt, leading to a thick layer of cold glass and possibly blocking the discharge port. Optimizations of the crucible bottom structure and melting process are therefore essential. Numerical simulation has been widely used to provide theoretical guidance for cold crucible structure design and melting process research. In this work, we applied the electromagnetic induction models to investigate the heating efficiency of different bottom structures of cold crucibles. In addition, a magneto-thermo-fluid model was applied to study the temperature field and heat convection of glass melt under induction heating. Moreover, the flow field with and without agitation were also compared, using Frozen rotor approach to accelerate the flow field calculation. The results show that increasing the slit width can enhance the magnetic field inside the crucible, reduce the electromagnetic, and increase the heating efficiency of the glass melt by about 6%. In addition, increasing the slit length can increase the magnetic induction intensity and heating efficiency of the glass near the discharge port. The maximum temperature near the bottom of the crucible is only 330 ℃ due to the combination of the weak magnetic field and water cooling. The flow velocity of the glass melt near the bottom is low because of the low temperature. The velocity of fluid near the bottom increases by one order of magnitude to 0.1 m/s under mechanical agitation. Based on the numerical simulation results, the optimized structure design of the cold crucible bottom and agitator improve the temperature and flow velocity near the discharge port and the discharge efficiency.