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.
Bibliographical noteFunding Information:
Funding: The author (J.W.) was supported by the China Scholarship Council (201808260026). The author (C.L.) was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2019R1A6A3A13094308). The corresponding author (J.K.) expresses thanks for the support from the BK21 PLUS program.
© 2020 by the authors.
- Crystal growth
- Dendritic pattern formation
- Laplace-Beltrami operator
- Phase-field model
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- Physics and Astronomy (miscellaneous)