Abstract
In this paper, we present a numerical method for the phase-field model of anisotropic ice crystal growth on a spherical surface. The mathematical model includes terms related to the anisotropic interfacial energy, which is defined by the interface angle with respect to a reference angle. One of the natural numerical methods on curved surfaces is a computational technique based on a triangular mesh for the surface in a three-dimensional space. However, it is difficult to compute terms with the interface angle on a triangular mesh. To resolve this problem, we solve the governing equation in Cartesian coordinates after rotating each vertex and the 1-ring neighborhood of the vertex on the triangular mesh. After rotation and interpolation, we numerically solve the phase-field model using a standard finite difference method. We present the results of several tests to demonstrate that the proposed algorithm can recover anisotropic ice crystal growth on a spherical surface.
Original language | English |
---|---|
Pages (from-to) | 25-33 |
Number of pages | 9 |
Journal | Computers and Mathematics with Applications |
Volume | 125 |
DOIs | |
Publication status | Published - 2022 Nov 1 |
Bibliographical note
Funding Information:The first author (C. Lee) was supported by the Brain Korea 21 (BK21) FOUR from the Ministry of Education of Korea. S. Yoon was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT of Korea ( MSIT ) (No. 2019R1A6A1A11051177 ). H. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2020R1A6A3A13077105 ). Y.B. Li is supported by National Natural Science Foundation of China (No. 11871056 , No. 11631012 ). D. Jeong was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2020R1F1A1A01075937 ). The corresponding author (J. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2019R1A2C1003053 ). The authors are grateful to the reviewers for their constructive comments on this article.
Publisher Copyright:
© 2022 Elsevier Ltd
Keywords
- Ice crystal growth
- Phase-field model
- Spherical surface
ASJC Scopus subject areas
- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics