An enthalpy formulation for phase change problems with a large thermal diffusivity jump across the interface

An enthalpy formulation is proposed in the present investigation for a phase change material (PCM) having a distinct freezing temperature. The latent heat is separated from the sensible heat such that there exists a dependent variable (the sensible heat) that is a continuous function over the entire physical domain. Inside each control volume, the latent heat is rigorously evaluated from the fraction of the liquid phase to achieve an even latent heat evolution. In the dimensionless transformation, the characteristic time is denned in terms of the Stefan number. The coefficients of the unsteady terms thus are always less than unity. This will achieve a good numerical stability for any Stefan number. In addition, this particular transformation makes the present enthalpy formulation applicable to single phase problems if an infinite Stefan number is assigned. To account for a thermal diffusivity jump at the liquid-solid interface, a modified weighting function scheme is developed. Through a few examples, the present enthalpy formulation is seen to produce an accurate and smooth liquid-solid interface for PCM having a distinct freezing point.