A second-order accurate non-linear difference scheme for the N -component Cahn-Hilliard system

Hyun Geun Lee, Junseok Kim

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


We consider a second-order conservative nonlinear numerical scheme for the N-component Cahn-Hilliard system modeling the phase separation of a N-component mixture. The scheme is based on a Crank-Nicolson finite-difference method and is solved by an efficient and accurate nonlinear multigrid method. We numerically demonstrate the second-order accuracy of the numerical scheme. We observe that our numerical solutions are consistent with the exact solutions of linear stability analysis results. We also describe numerical experiments such as the evolution of triple junctions and the spinodal decomposition in a quaternary mixture. We investigate the effects of a concentration dependent mobility on phase separation.

Original languageEnglish
Pages (from-to)4787-4799
Number of pages13
JournalPhysica A: Statistical Mechanics and its Applications
Issue number19-20
Publication statusPublished - 2008 Aug

Bibliographical note

Funding Information:
This research was supported by the MKE (Ministry of Knowledge Economy), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute for Information Technology Advancement) (IITA-2008- C1090-0801-0013). This work was also supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-C00225).


  • Finite difference
  • N-component Cahn-Hilliard
  • Nonlinear multigrid
  • Phase separation

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics


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