Phase-field computations of anisotropic ice crystal growth on a spherical surface

Chaeyoung Lee; Sungha Yoon; Jintae Park; Hyundong Kim; Yibao Li; Darae Jeong; Sangkwon Kim; Soobin Kwak; Junseok Kim

doi:10.1016/j.camwa.2022.08.035

Phase-field computations of anisotropic ice crystal growth on a spherical surface

Chaeyoung Lee, Sungha Yoon, Jintae Park, Hyundong Kim, Yibao Li, Darae Jeong, Sangkwon Kim, Soobin Kwak, Junseok Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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	https://doi.org/10.1016/j.camwa.2022.08.035
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

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10.1016/j.camwa.2022.08.035

Cite this

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title = "Phase-field computations of anisotropic ice crystal growth on a spherical surface",

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.",

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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: {\textcopyright} 2022 Elsevier Ltd",

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AU - Lee, Chaeyoung

AU - Yoon, Sungha

AU - Park, Jintae

AU - Kim, Hyundong

AU - Li, Yibao

AU - Jeong, Darae

AU - Kim, Sangkwon

AU - Kwak, Soobin

AU - Kim, Junseok

N1 - 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

PY - 2022/11/1

Y1 - 2022/11/1

N2 - 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.

AB - 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.

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JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

ER -

Phase-field computations of anisotropic ice crystal growth on a spherical surface

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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