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

4 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

Keywords

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

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)

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