Journal of the Korean Society for Industrial and Applied Mathematics

  • 제16권1호
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  • Pages.15-29
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  • 2012
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
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A ROBUST AND ACCURATE PHASE-FIELD SIMULATION OF SNOW CRYSTAL GROWTH

  • 투고 : 2011.08.19
  • 심사 : 2012.03.05
  • 발행 : 2012.03.25
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초록

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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참고문헌

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피인용 문헌

  1. A NUMERICAL METHOD FOR THE MODIFIED VECTOR-VALUED ALLEN-CAHN PHASE-FIELD MODEL AND ITS APPLICATION TO MULTIPHASE IMAGE SEGMENTATION vol.18, pp.1, 2014, https://doi.org/10.12941/jksiam.2014.18.027
  2. Fourier-Spectral Method for the Phase-Field Equations vol.8, pp.8, 2020, https://doi.org/10.3390/math8081385