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http://dx.doi.org/10.12941/jksiam.2012.16.1.015

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

Li, Yibao (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
Lee, Dong-Sun (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
Lee, Hyun-Geun (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
Jeong, Da-Rae (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
Lee, Chae-Young (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
Yang, Dong-Gyu (SEOUL SCIENCE HIGH SCHOOL)
Kim, Jun-Seok (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.16, no.1, 2012 , pp. 15-29 More about this Journal
Abstract
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 accuracy and efficiency of the method for snow crystal growth.
Keywords
Allen-Cahn equation; phase-field method; Wulff construction; snow crystal growth;
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