TY - JOUR
T1 - A conservative finite difference scheme for the N-component Cahn–Hilliard system on curved surfaces in 3D
AU - Yang, Junxiang
AU - Li, Yibao
AU - Lee, Chaeyoung
AU - Jeong, Darae
AU - Kim, Junseok
N1 - Funding Information:
The author (D. Jeong) was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (NRF-2017R1E1A1A03070953). Y.B. Li is supported by National Natural Science Foundation of China (Nos. 11601416, 11631012). The corresponding author (J.S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B03933243). The authors appreciate the reviewers for their constructive comments, which have improved the quality of this paper. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - 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- 1) 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.
AB - 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- 1) 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.
KW - Closest point method
KW - Conservative scheme
KW - N-component Cahn–Hilliard equation
KW - Narrow band domain
UR - http://www.scopus.com/inward/record.url?scp=85074862832&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85074862832&partnerID=8YFLogxK
U2 - 10.1007/s10665-019-10023-9
DO - 10.1007/s10665-019-10023-9
M3 - Article
AN - SCOPUS:85074862832
VL - 119
SP - 149
EP - 166
JO - Journal of Engineering Mathematics
JF - Journal of Engineering Mathematics
SN - 0022-0833
IS - 1
ER -