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We investigate a family of phase field models for simulating dendritic growthof a pure supercooled substance. The central object of interest is the reactionterm in the Allen-Cahn equation, which is responsible for spatial distributionof latent heat release during solidification. In this context, several existingforms of the reaction term are analyzed. Inspired by the known conclusions ofmatched asymptotic analysis, we propose new variants that are simple enough toallow mathematical and numerical analysis and robust enough to be applicable tosolidification under very large supercooling. The resulting models are testedin a number of numerical simulations focusing on mesh-dependence and modelparameter settings. Despite the phase interface thickness being relativelylarge to make numerical computations feasible, the obtained results exhibit agood quantitative agreement with experimental data from rapid solidification ofnickel melts.

Focusing the Latent Heat Release in 3D Phase Field Simulations of Dendritic Crystal Growth