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

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 statusAccepted/In press - 2022

Keywords

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

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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