Effective time step analysis of a nonlinear convex splitting scheme for the Cahn–Hilliard equation

Seunggyu Lee, Junseok Kim

    Research output: Contribution to journalArticlepeer-review

    13 Citations (Scopus)

    Abstract

    We analyze the effective time step size of a nonlinear convex splitting scheme for the Cahn–Hilliard (CH) equation. The convex splitting scheme is unconditionally stable, which implies we can use arbitrary large time-steps and get stable numerical solutions. However, if we use a too large time-step, then we have not only discretization error but also time-step rescaling problem. In this paper, we show the time-step rescaling problem from the convex splitting scheme by comparing with a fully implicit scheme for the CH equation. We perform various test problems. The computation results confirm the time-step rescaling problem and suggest that we need to use small enough time-step sizes for the accurate computational results.

    Original languageEnglish
    Pages (from-to)448-460
    Number of pages13
    JournalComunicata Scientiae
    Volume25
    Issue number2
    DOIs
    Publication statusPublished - 2019 Feb

    Bibliographical note

    Publisher Copyright:
    © 2019 Global-Science Press

    Keywords

    • Cahn–Hilliard equation
    • Convex splitting
    • Effective time step
    • Fourier analysis

    ASJC Scopus subject areas

    • General Agricultural and Biological Sciences

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