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A ROBUST AND ACCURATE PHASE-FIELD SIMULATION OF SNOW CRYSTAL GROWTHA ROBUST AND ACCURATE PHASE-FIELD SIMULATION OF SNOW CRYSTAL GROWTH
- Other Titles
- A ROBUST AND ACCURATE PHASE-FIELD SIMULATION OF SNOW CRYSTAL GROWTH
- Issue Date
- 2012
- Publisher
- 한국산업응용수학회
- Keywords
- Allen–Cahn equation; phase-field method; Wulff construction; snow crystal growth
- Citation
- Journal of the Korean Society for Industrial and Applied Mathematics, v.16, no.1, pp.15 - 29
- Indexed
- KCI
- Volume
- 16
- Number
- 1
- Start Page
- 15
- End Page
- 29
- ISSN
- 1226-9433
- 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.
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