A numerical method for the ternary Cahn-Hilliard system with a degenerate mobility

Junseok Kim, Kyungkeun Kang

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


We applied a second-order conservative nonlinear multigrid method for the ternary Cahn-Hilliard system with a concentration dependent degenerate mobility for a model for phase separation in a ternary mixture. First, we used a standard finite difference approximation for spatial discretization and a Crank-Nicolson semi-implicit scheme for the temporal discretization. Then, we solved the resulting discretized equations using an efficient nonlinear multigrid method. We proved stability of the numerical solution for a sufficiently small time step. We demonstrate the second-order accuracy of the numerical scheme. We also show that our numerical solutions of the ternary Cahn-Hilliard system are consistent with the exact solutions of the linear stability analysis results in a linear regime. We demonstrate that the multigrid solver can straightforwardly deal with different boundary conditions such as Neumann, periodic, mixed, and Dirichlet. Finally, we describe numerical experiments highlighting differences of constant mobility and degenerate mobility in one, two, and three spatial dimensions.

Original languageEnglish
Pages (from-to)1029-1042
Number of pages14
JournalApplied Numerical Mathematics
Issue number5
Publication statusPublished - 2009 May

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). The second author was supported partially by KRF-2006-331-C00020.

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'A numerical method for the ternary Cahn-Hilliard system with a degenerate mobility'. Together they form a unique fingerprint.

Cite this