A compact fourth-order finite difference scheme for the three-dimensional Cahn-Hilliard equation

Yibao Li, Hyun Geun Lee, Binhu Xia, Junseok Kim

Research output: Contribution to journalArticle

24 Citations (Scopus)


This work extends the previous two-dimensional compact scheme for the Cahn-Hilliard equation (Lee et al., 2014) to three-dimensional space. The proposed scheme, derived by combining a compact formula and a linearly stabilized splitting scheme, has second-order accuracy in time and fourth-order accuracy in space. The discrete system is conservative and practically stable. We also implement the compact scheme in a three-dimensional adaptive mesh refinement framework. The resulting system of discrete equations is solved by using a multigrid. We demonstrate the performance of our proposed algorithm by several numerical experiments.

Original languageEnglish
Pages (from-to)108-116
Number of pages9
JournalComputer Physics Communications
Publication statusPublished - 2016 Mar 1



  • Adaptive mesh refinement
  • Cahn-Hilliard equation
  • Finite difference method
  • Fourth-order compact scheme
  • Multigrid

ASJC Scopus subject areas

  • Hardware and Architecture
  • Physics and Astronomy(all)

Cite this