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A conservative numerical method for the Cahn-Hilliard equation with Dirichlet boundary conditions in complex domains

Authors
Li, YibaoJeong, DaraeShin, JaeminKim, Junseok
Issue Date
1월-2013
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
Keywords
Cahn-Hilliard equation; Dirichlet boundary condition; Complex domain; Unconditionally gradient stable scheme; Multigrid method
Citation
COMPUTERS & MATHEMATICS WITH APPLICATIONS, v.65, no.1, pp.102 - 115
Indexed
SCIE
SCOPUS
Journal Title
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume
65
Number
1
Start Page
102
End Page
115
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/104395
DOI
10.1016/j.camwa.2012.08.018
ISSN
0898-1221
Abstract
In this paper we present a conservative numerical method for the Cahn-Hilliard equation with Dirichlet boundary conditions in complex domains. The method uses an unconditionally gradient stable nonlinear splitting numerical scheme to remove the high-order time-step stability constraints. The continuous problem has the conservation of mass and we prove the conservative property of the proposed discrete scheme in complex domains. We describe the implementation of the proposed numerical scheme in detail. The resulting system of discrete equations is solved by a nonlinear multigrid method. We demonstrate the accuracy and robustness of the proposed Dirichlet boundary formulation using various numerical experiments. We numerically show the total energy decrease and the unconditionally gradient stability. In particular, the numerical results indicate the potential usefulness of the proposed method for accurately calculating biological membrane dynamics in confined domains. (c) 2012 Elsevier Ltd. All rights reserved.
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