Abstract
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 language | English |
|---|---|
| Pages (from-to) | 510-522 |
| Number of pages | 13 |
| Journal | Physica A: Statistical Mechanics and its Applications |
| Volume | 442 |
| DOIs | |
| Publication status | Published - 2016 Jan 15 |
Bibliographical note
Funding Information:The first author (D. Jeong) was supported by a Korea University Grant. 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 ). The authors would like to thank the reviewers for their comments that help improve the manuscript.
Keywords
- Finite difference method
- Logarithmic free energy
- Multigrid method
- Phase separation
- Ternary Cahn-Hilliard
ASJC Scopus subject areas
- Statistics and Probability
- Condensed Matter Physics