An implicit fixed-grid method for the finite-element analysis of heat transfer involving phase changes

The finite-element method is widely used for thermal numerical simulation of heat treatment, casting, or welding processes. The modeling of phase changes requires the simulation of highly nonlinear problems due to latent heat effects. In this article, a finite-element procedure is developed for modeling latent heat effects using an implicit time discretization for transient heat conduction problems involving phase changes for which the enthalpy can be supposed to be a function of temperature only. It is also developed for stationary convection-diffusion problems. Examples are presented to show the efficiency of the method for isothermal and anisothermal transformations. Finally, the method is extended to take couplings with metallurgical transformation kinetics into account.