The aim of this study is to perform numerical simulation of a vitrification process developed by the French Atomic Commission and Areva NC. This process uses the direct induction technology in a cold crucible to melt specific glass at a high temperature ( ∼ 1250\degC). The numerical simulation of this process needs a coupled approach of different phenomena: induction, thermal and hydrodynamic. Indeed, those three phenomena are strongly coupled because of the temperature dependence of the glass properties. For example, the hotter the molten glass, the higher the electrical conductivity. Two softwares are used to achieve the purpose of the study. Thermal and hydrodynamic aspects are modeled using FLUENT\circledR whereas induction is modeled using FLUX\circledR A homemade iterative coupling is performed between the two softwares, which leads to a full 3D simulation of the molten glass heated by induction. In order to validate the coupling, a simplified configuration is studied, in which mechanical stirring and air bubbling are not modeled. Only buoyancy and Marangoni convection are taken into account. A complex thermoconvective flow configuration appears within the glass bath, when the total Joule power injected reaches a specific threshold. Qualitative comparison of the aspect of free surface is performed. The direct measurement of the temperature in the glass bath gives a quantitative comparison between experimental and numerical results. A reasonably good agreement is found in both cases. Tables 1, Figs 7, Refs 5.