A ROBUST AND ACCURATE PHASE-FIELD SIMULATION OF SNOW CRYSTAL GROWTH

Yibao Li, Dong-Sun Lee, Hyun-Geun Lee, Da-Rae Jeong, Chae-Young Lee, Dong-Gyu Yang, Jun-Seok Kim
2012 Journal of the Korea Society for Industrial and Applied Mathematics  
In this paper we introduce 6-fold symmetry crystal growth using new phase-field models based on the modified Allen-Cahn equation. The proposed method is a hybrid method which uses both analytic and numerical solutions. We then show this method can be extended to k-fold case. The Wulff construction procedure is provided to understand and predict the shape of crystals. We also present a detailed mathematical proof of the validity of the Wulff construction. For computational results, we verify the
more » ... accuracy and efficiency of the method for snow crystal growth.
doi:10.12941/jksiam.2012.16.1.015 fatcat:dcohz6fh7vfmfkpg4n7jkcrasm