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 |
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Keywords
- Finite difference method
- Logarithmic free energy
- Multigrid method
- Phase separation
- Ternary Cahn-Hilliard
ASJC Scopus subject areas
- Condensed Matter Physics
- Statistics and Probability
Cite this
A practical numerical scheme for the ternary Cahn-Hilliard system with a logarithmic free energy. / Jeong, Darae; Kim, Junseok.
In: Physica A: Statistical Mechanics and its Applications, Vol. 442, 15.01.2016, p. 510-522.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A practical numerical scheme for the ternary Cahn-Hilliard system with a logarithmic free energy
AU - Jeong, Darae
AU - Kim, Junseok
PY - 2016/1/15
Y1 - 2016/1/15
N2 - 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.
AB - 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.
KW - Finite difference method
KW - Logarithmic free energy
KW - Multigrid method
KW - Phase separation
KW - Ternary Cahn-Hilliard
UR - http://www.scopus.com/inward/record.url?scp=84943644630&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84943644630&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2015.09.038
DO - 10.1016/j.physa.2015.09.038
M3 - Article
VL - 442
SP - 510
EP - 522
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
SN - 0378-4371
ER -