Convex Splitting Runge–Kutta methods for phase-field models

Jaemin Shin, Hyun Geun Lee, June Yub Lee

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

In this paper, we present the Convex Splitting Runge–Kutta (CSRK) methods which provide a simple unified framework to solve phase-field models such as the Allen–Cahn, Cahn–Hilliard, and phase-field crystal equations. The core idea of the CSRK methods is the combination of convex splitting methods and multi-stage implicit–explicit Runge–Kutta methods. Our CSRK methods are high-order accurate in time and we investigate the energy stability numerically. We present numerical experiments to show the accuracy and efficiency of the proposed methods up to the third-order accuracy.

Original languageEnglish
Pages (from-to)2388-2403
Number of pages16
JournalComputers and Mathematics with Applications
Volume73
Issue number11
DOIs
StatePublished - 1 Jun 2017

Keywords

  • Allen–Cahn equation
  • Cahn–Hilliard equation
  • Convex splitting
  • Implicit–explicit Runge–Kutta
  • Phase-field crystal equation

Fingerprint

Dive into the research topics of 'Convex Splitting Runge–Kutta methods for phase-field models'. Together they form a unique fingerprint.

Cite this