A practical and efficient numerical method for the Cahn–Hilliard equation in complex domains

Darae Jeong; Junxiang Yang; Junseok Kim

doi:10.1016/j.cnsns.2019.02.009

A practical and efficient numerical method for the Cahn–Hilliard equation in complex domains

Darae Jeong, Junxiang Yang, Junseok Kim

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26 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	217-228
Number of pages	12
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	73
DOIs	https://doi.org/10.1016/j.cnsns.2019.02.009
Publication status	Published - 2019 Jul 15

Bibliographical note

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 ).

Publisher Copyright:
© 2019 Elsevier B.V.

Keywords

Cahn–Hilliard equation
Complex domain
Multigrid method
Phase separation
Ternary Cahn–Hilliard system

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Applied Mathematics

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10.1016/j.cnsns.2019.02.009

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title = "A practical and efficient numerical method for the Cahn–Hilliard equation in complex domains",

abstract = "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.",

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author = "Darae Jeong and Junxiang Yang and Junseok Kim",

note = "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 ). Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

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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.

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A practical and efficient numerical method for the Cahn–Hilliard equation in complex domains

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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