Effective time step analysis for the Allen–Cahn equation with a high-order polynomial free energy

Seunggyu Lee, Sungha Yoon, Chaeyoung Lee, Sangkwon Kim, Hyundong Kim, Junxiang Yang, Soobin Kwak, Youngjin Hwang, Junseok Kim

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)

    Abstract

    An effective time step analysis to the linear convex splitting scheme for the Allen–Cahn equation with a high-order polynomial free energy is presented in this article. Although the convex splitting scheme is unconditionally stable, using a large time step causes a time step rescaling effect, leading to delayed dynamics of the governing equation. We verify this problem by comparing it with a reformulated semi-implicit scheme using the effective time step. Theoretical results show that the discrete energy stability and maximum-principle hold, and the numerical results demonstrate that the time step rescaling issue can be resolved using the effective time step. We confirm that slow dynamics due to high-order potential is alleviated by the time step modification through the results of motion by mean curvature.

    Original languageEnglish
    Pages (from-to)4726-4743
    Number of pages18
    JournalInternational Journal for Numerical Methods in Engineering
    Volume123
    Issue number19
    DOIs
    Publication statusPublished - 2022 Oct 15

    Bibliographical note

    Funding Information:
    information Ministry of Education, Grant/Award Number: NRF-2020R1A6A3A13077105; Ministry of Science and ICT, South Korea, Grant/Award Number: 2019R1A6A1A11051177; Ministry of Science, ICT and Future Planning, Grant/Award Number: 2020R1A2C1A01100114The first author (Seunggyu Lee) was supported by a Korea University Grant and the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (No. 2020R1A2C1A01100114). 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). The author (Hyundong Kim) was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Republic of Korea (NRF-2020R1A6A3A13077105). The corresponding author (Junseok Kim) was supported by a Grant from the Korea University Grant. The authors are grateful to the reviewers for their contributions to improving this article.

    Publisher Copyright:
    © 2022 John Wiley & Sons Ltd.

    Keywords

    • Allen–Cahn equation
    • effective time step
    • high-order polynomial free energy
    • linear convex splitting

    ASJC Scopus subject areas

    • Numerical Analysis
    • General Engineering
    • Applied Mathematics

    Fingerprint

    Dive into the research topics of 'Effective time step analysis for the Allen–Cahn equation with a high-order polynomial free energy'. Together they form a unique fingerprint.

    Cite this