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A linear convex splitting scheme for the Cahn-Hilliard equation with a high-order polynomial free energy

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Title
A linear convex splitting scheme for the Cahn-Hilliard equation with a high-order polynomial free energy
Author(s)
Seunggyu Lee; Yoon, Sungha; Kim, Junseok
Publication Date
2023-09
Journal
International Journal for Numerical Methods in Engineering, v.124, no.17, pp.3586 - 3602
Publisher
John Wiley & Sons Inc.
Abstract
In this article, we present an unconditionally energy stable linear scheme for the Cahn-Hilliard equation with a high-order polynomial free energy. The classical Cahn-Hilliard equation does not satisfy the maximum principle; hence the order parameter can be shifted out of the minimum values of the double-well potential. We adopt a high-order polynomial potential to diminish this effect and employ the efficient linear convex splitting scheme. Since the stabilizing factor gradually increases as the degree of potential becomes greater, we modify a non-physical part of potential as a fourth-order polynomial to reduce the stabilizing factor. Numerical results as well as theoretical results demonstrate the accuracy and energy stability of our method. Furthermore, we verify that some limitations arising from applications of the classical Cahn-Hilliard model can be resolved by adopting a high-order free energy.
URI
https://pr.ibs.re.kr/handle/8788114/13794
DOI
10.1002/nme.7288
ISSN
0029-5981
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > 1. Journal Papers (저널논문)
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