I am not familiar with Fluent and cannot say anything about solution methods but the main challenge is first to compose the adequate model of melting that would take into account very specific features of the event like constant temperature within the melting front due to coexistence of solid and liquid phase, melting front propagation, the fact that velocity of front propagation is solely defined by the rate of heat transfer to the front, etc.
After devising such a model it is time to think about formal methods of its solution.
You can try ANSYS APDL/workbench to simulate the phase change model. A detailed description of the Theory that involves the enthalpy method and the modelling of temperature-dependent material property is presented in the ANSYS Help file. A good GUI demonstration is also done in this help file (Page no A-1-15 to A-1-28). In my opinion, It may be quite helpful in finishing your work. The link is provided below