In the framework of the MUSIC-haic European project, the ONERA 3D accretion solver Film has been enhanced with ICI (Ice Crystal Icing) capabilities. These new features target different phenomena such as ice layer porosity, erosion due to ice crystals impacts, and also heat transfers with the solid surface. In ICI simulations, the erosion phenomena plays an active role on the ice shape, creating conical shapes which have been extensively studied. However, these shapes are currently modeled using a multi-step approach which requires a re-meshing procedure at each time step. Such a procedure, involving recomputing the flow-field and particle trajectories, would be very expensive for 3D simulations. The first part of this article is then devoted to present a new geometrical approach which is promising to take into account the erosion effect on the ice shape for 3D simulations without re-meshing. The other key point for ICI simulations is the modeling of thermal coupling with the wall. Indeed, this phenomenon is essential for simulations in engine environment or on anti-iced airfoils. The second part of the article is then dedicated to the implementation of an efficient algorithm for the thermal coupling with a 3D heat conduction solver.