A conservative finite difference scheme for the N-component Cahn-Hilliard system on curved surfaces in 3D
- Authors
- Yang, Junxiang; Li, Yibao; Lee, Chaeyoung; Jeong, Darae; Kim, Junseok
- Issue Date
- 12월-2019
- Publisher
- SPRINGER
- Keywords
- Closest point method; Conservative scheme; N-component Cahn-Hilliard equation; Narrow band domain
- Citation
- JOURNAL OF ENGINEERING MATHEMATICS, v.119, no.1, pp.149 - 166
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF ENGINEERING MATHEMATICS
- Volume
- 119
- Number
- 1
- Start Page
- 149
- End Page
- 166
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/61414
- DOI
- 10.1007/s10665-019-10023-9
- ISSN
- 0022-0833
- Abstract
- This paper presents a conservative finite difference scheme for solving the N-component Cahn-Hilliard (CH) system on curved surfaces in three-dimensional (3D) space. Inspired by the closest point method (Macdonald and Ruuth, SIAM J Sci Comput 31(6):4330-4350, 2019), we use the standard seven-point finite difference discretization for the Laplacian operator instead of the Laplacian-Beltrami operator. We only need to independently solve (N-) CH equations in a narrow band domain around the surface because the solution for the Nth component can be obtained directly. The N-component CH system is discretized using an unconditionally stable nonlinear splitting numerical scheme, and it is solved by using a Jacobi-type iteration. Several numerical tests are performed to demonstrate the capability of the proposed numerical scheme. The proposed multicomponent model can be simply modified to simulate phase separation in a complex domain on 3D surfaces.
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