Focusing the latent heat release in 3D phase field simulations of dendritic crystal growth

Abstract

We investigate a family of phase field models for simulating dendritic growth of a pure supercooled substance. The central object of interest is the reaction term in the Allen–Cahn equation, which is responsible for the spatial distribution of latent heat release during solidification. In this context, several existing forms of the reaction term are analyzed. Inspired by the known conclusions of matched asymptotic analysis, we propose a new variant (the ‘ΣP1-P’ model) that is simple enough to allow mathematical and numerical analysis and robust enough to be applicable to solidification under very large supercooling. The important component of the model (the Σ limiter) can also be incorporated into the original models to extend the range of their applicability. The individual models are tested in a number of numerical simulations focusing on mesh-dependence and model parameter settings. When the phase interface thickness is kept large with respect to the microscopic capillary length to make numerical computations feasible, the parameters of the Σ limiter can be tuned to improve agreement with previous models. The results obtained using the ΣP1-P model exhibit a good quantitative agreement with experimental data from rapid solidification of nickel melts.