Focusing the Latent Heat Release in 3D Phase Field Simulations of Dendritic Crystal Growth
arXiv:2010.05664 · doi:10.1088/1361-651X/ac0f55
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 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 new variants that are simple enough to allow mathematical and numerical analysis and robust enough to be applicable to solidification under very large supercooling. The resulting models are tested in a number of numerical simulations focusing on mesh-dependence and model parameter settings. Despite the phase interface thickness being relatively large to make numerical computations feasible, the obtained results exhibit a good quantitative agreement with experimental data from rapid solidification of nickel melts.
v4: Substantial improvements and reformulations of the text AND the abstract. This revision is based on the reviewer's report we received as the paper was rejected by Elsevier's Computational Materials Science. However, the results remain valid. The resulting improved text has been submitted to IOP Science's MSMSE