A practical numerical scheme for the ternary Cahn-Hilliard system with a logarithmic free energy

Darae Jeong, Junseok Kim

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7 Citations (Scopus)


We consider a practically stable finite difference method for the ternary Cahn-Hilliard system with a logarithmic free energy modeling the phase separation of a three-component mixture. The numerical scheme is based on a linear unconditionally gradient stable scheme by Eyre and is solved by an efficient and accurate multigrid method. The logarithmic function has a singularity at zero. To remove the singularity, we regularize the function near zero by using a quadratic polynomial approximation. We perform a convergence test, a linear stability analysis, and a robustness test of the ternary Cahn-Hilliard equation. We observe that our numerical solutions are convergent, consistent with the exact solutions of linear stability analysis, and stable with practically large enough time steps. Using the proposed numerical scheme, we also study the temporal evolution of morphology patterns during phase separation in one-, two-, and three-dimensional spaces.

Original languageEnglish
Pages (from-to)510-522
Number of pages13
JournalPhysica A: Statistical Mechanics and its Applications
Publication statusPublished - 2016 Jan 15



  • Finite difference method
  • Logarithmic free energy
  • Multigrid method
  • Phase separation
  • Ternary Cahn-Hilliard

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistics and Probability

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