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Numerical Simulation of Dendritic Pattern Formation in an Isotropic Crystal Growth Model on Curved Surfaces

Authors
Yoon, SunghaPark, JintaeWang, JianLee, ChaeyoungKim, Junseok
Issue Date
7월-2020
Publisher
MDPI
Keywords
crystal growth; Laplace-Beltrami operator; phase-field model; dendritic pattern formation
Citation
SYMMETRY-BASEL, v.12, no.7
Indexed
SCIE
SCOPUS
Journal Title
SYMMETRY-BASEL
Volume
12
Number
7
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/54870
DOI
10.3390/sym12071155
ISSN
2073-8994
Abstract
In this paper, we present several numerical simulation results of dendritic pattern formation using an isotropic crystal growth model, which is based on phase-field modeling, on curved surfaces. An explicit time-stepping method is used and the direct computing method to the Laplace-Beltrami operator, which employs the point centered triangulation approximating Laplacian over the discretized surface with a triangular mesh, is adopted. Numerical simulations are performed not only on simple but also on complex surfaces with various curvatures, and the proposed method can simulate dendritic growth on complex surfaces. In particular, ice crystal growth simulation results on aircraft fuselage or metal bell-shaped curved surfaces are provided in order to demonstrate the practical relevance to our dendrite growth model. Furthermore, we perform several numerical parameter tests to obtain a best fitted set of parameters on simple surfaces. Finally, we apply this set of parameters to numerical simulation on complex surfaces.
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