A conservative numerical method for the Cahn-Hilliard equation with Dirichlet boundary conditions in complex domains

Yibao Li, Darae Jeong, Jaemin Shin, Junseok Kim

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

In this paper we present a conservative numerical method for the Cahn-Hilliard equation with Dirichlet boundary conditions in complex domains. The method uses an unconditionally gradient stable nonlinear splitting numerical scheme to remove the high-order time-step stability constraints. The continuous problem has the conservation of mass and we prove the conservative property of the proposed discrete scheme in complex domains. We describe the implementation of the proposed numerical scheme in detail. The resulting system of discrete equations is solved by a nonlinear multigrid method. We demonstrate the accuracy and robustness of the proposed Dirichlet boundary formulation using various numerical experiments. We numerically show the total energy decrease and the unconditionally gradient stability. In particular, the numerical results indicate the potential usefulness of the proposed method for accurately calculating biological membrane dynamics in confined domains.

Original languageEnglish
Pages (from-to)102-115
Number of pages14
JournalComputers and Mathematics with Applications
Volume65
Issue number1
DOIs
Publication statusPublished - 2013 Jan

Keywords

  • Cahn-Hilliard equation
  • Complex domain
  • Dirichlet boundary condition
  • Multigrid method
  • Unconditionally gradient stable scheme

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Fingerprint Dive into the research topics of 'A conservative numerical method for the Cahn-Hilliard equation with Dirichlet boundary conditions in complex domains'. Together they form a unique fingerprint.

  • Cite this