TY - JOUR
T1 - A practical and efficient numerical method for the Cahn–Hilliard equation in complex domains
AU - Jeong, Darae
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 ). The corresponding author (Junseok Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF- 2016R1D1A1B03933243 ).
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). The corresponding author (Junseok Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B03933243).
PY - 2019/7/15
Y1 - 2019/7/15
N2 - In this article, we present a practical and efficient numerical method for the Cahn–Hilliard (CH) equation in the two- and three-dimensional complex domains. We propose a simple mathematical model for the binary mixture in the complex domains. The model is based on the ternary CH system. An arbitrary domain is represented by the third phase, which is fixed during the temporal evolution of the other phases. By the local conservative property of the sum of the phases, the governing equation is simplified to a binary CH equation with a source term. For the numerical solution, we use a practically unconditionally gradient stable scheme. Various numerical experiments are performed on arbitrary domains. The numerical results show that the proposed algorithm can deal with the complex domains efficiently.
AB - In this article, we present a practical and efficient numerical method for the Cahn–Hilliard (CH) equation in the two- and three-dimensional complex domains. We propose a simple mathematical model for the binary mixture in the complex domains. The model is based on the ternary CH system. An arbitrary domain is represented by the third phase, which is fixed during the temporal evolution of the other phases. By the local conservative property of the sum of the phases, the governing equation is simplified to a binary CH equation with a source term. For the numerical solution, we use a practically unconditionally gradient stable scheme. Various numerical experiments are performed on arbitrary domains. The numerical results show that the proposed algorithm can deal with the complex domains efficiently.
KW - Cahn–Hilliard equation
KW - Complex domain
KW - Multigrid method
KW - Phase separation
KW - Ternary Cahn–Hilliard system
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U2 - 10.1016/j.cnsns.2019.02.009
DO - 10.1016/j.cnsns.2019.02.009
M3 - Article
AN - SCOPUS:85061667187
VL - 73
SP - 217
EP - 228
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
ER -