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 journalArticlepeer-review

47 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

Bibliographical note

Funding Information:
Y.B. Li is supported by the Fundamental Research Funds for the Central Universities, China (No. XJJ2015068 ) and supported by China Postdoctoral Science Foundation (No. 2015M572541 ). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2014R1A2A2A01003683 ).

Publisher Copyright:
© 2015 Elsevier B.V.

Copyright 2016 Elsevier B.V., All rights reserved.


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

ASJC Scopus subject areas

  • Hardware and Architecture
  • General Physics and Astronomy


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