Comparison of implicit enthalpy methods for Stefan problems

Enthalpy methods are a class of fixed-mesh schemes for the solution of Stefan problems that are based on the enthalpy formulation of the energy conservation equation. When they are combined with implicit time discretizations, a nonlinear system involving total enthalpies and temperatures must be solved at each instant of time. The system is complex to solve because the enthalpy is given by a multivalued function of the temperature at the phase change. However, its efficient solution is critical for the performance of the overall method. In this article, we assess this point by reviewing and comparing three different solution strategies found in the literature.