TY - JOUR
T1 - A conservative numerical method for the Cahn-Hilliard equation with generalized mobilities on curved surfaces in three-dimensional space
AU - Jeong, Darae
AU - Li, Yibao
AU - Lee, Chaeyoung
AU - Yang, Junxiang
AU - Kim, Junseok
N1 - Funding Information:
The authors thank the reviewers for their constructive and helpful comments on the revision of this article. The first 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 (No.11601416, No.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).
Publisher Copyright:
© 2020 Global-Science Press.
PY - 2020
Y1 - 2020
N2 - In this paper, we develop a conservative numerical method for the Cahn-Hilliard equation with generalized mobilities on curved surfaces in three-dimensional space. We use an unconditionally gradient stable nonlinear splitting numerical scheme and solve the resulting system of implicit discrete equations on a discrete narrow band domain by using a Jacobi-type iteration. For the domain boundary cells, we use the trilinear interpolation using the closest point method. The proposing numerical algorithm is computationally efficient because we can use the standard finite difference Laplacian scheme on three-dimensional Cartesian narrow band mesh instead of discrete Laplace-Beltrami operator on triangulated curved surfaces. In particular, we employ a mass conserving correction scheme, which enforces conservation of total mass. We perform numerical experiments on the various curved surfaces such as sphere, torus, bunny, cube, and cylinder to demonstrate the performance and effectiveness of the proposed method. We also present the dynamics of the CH equation with constant and space-dependent mobilities on the curved surfaces.
AB - In this paper, we develop a conservative numerical method for the Cahn-Hilliard equation with generalized mobilities on curved surfaces in three-dimensional space. We use an unconditionally gradient stable nonlinear splitting numerical scheme and solve the resulting system of implicit discrete equations on a discrete narrow band domain by using a Jacobi-type iteration. For the domain boundary cells, we use the trilinear interpolation using the closest point method. The proposing numerical algorithm is computationally efficient because we can use the standard finite difference Laplacian scheme on three-dimensional Cartesian narrow band mesh instead of discrete Laplace-Beltrami operator on triangulated curved surfaces. In particular, we employ a mass conserving correction scheme, which enforces conservation of total mass. We perform numerical experiments on the various curved surfaces such as sphere, torus, bunny, cube, and cylinder to demonstrate the performance and effectiveness of the proposed method. We also present the dynamics of the CH equation with constant and space-dependent mobilities on the curved surfaces.
KW - Cahn-Hilliard equation
KW - Closest point method
KW - Mass correction scheme
KW - Narrow band domain
UR - http://www.scopus.com/inward/record.url?scp=85081331573&partnerID=8YFLogxK
U2 - 10.4208/cicp.OA-2018-0202
DO - 10.4208/cicp.OA-2018-0202
M3 - Article
AN - SCOPUS:85081331573
SN - 1815-2406
VL - 27
SP - 412
EP - 430
JO - Communications in Computational Physics
JF - Communications in Computational Physics
IS - 2
ER -