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

Seunggyu Lee, Sungha Yoon, Junseok Kim

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)3586-3602
Number of pages17
JournalInternational Journal for Numerical Methods in Engineering
Volume124
Issue number17
DOIs
Publication statusPublished - 2023 Sept 15

Bibliographical note

Funding Information:
The first author (Seunggyu Lee) was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (No. 2020R1A2C1A01100114) and “Regional Innovation Strategy (RIS)” through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (MOE) (No. 2022A‐02‐07‐02‐007). The author (Sungha Yoon) was supported by the National Research Foundation of Korea (NRF) Grant funded by the Ministry of Science and ICT of Korea (MSIT) (No. 2019R1A6A1A11051177) and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (MOE) (No. 2022R1I1A1A01073661). The corresponding author (Junseok Kim) was supported by Korea University Grant. The authors also wish to thank the reviewers for the constructive and helpful comments on the revision of this article.

Publisher Copyright:
© 2023 John Wiley & Sons Ltd.

Keywords

  • Cahn–Hilliard equation
  • high-order polynomial potential
  • linear convex splitting method
  • unconditionally energy stable

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics

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