triple point heat transfer gas, liquid, solid

Hello,

I want to know if it possible (or if it exists some tips) for modeling a triple point where gas, solid and liquid are in contact each over. At this point I have a huge loss of heat by conduction and I would to measure it and compare with experiment (and with over simulations where analytic functions describe the heat transfer coefficient near the triple point).

I try to reduce at maximum mesh size near this point, i have some issue with convergence when i decrease the parameter giving me the temperature width of the phase transition of my material. (Cp variation)

Some ideas?

Thank you