Abstract
We present a fourth-order spatial accurate and practically stable compact difference scheme for the Cahn-Hilliard equation. The compact scheme is derived by combining a compact nine-point formula and linearly stabilized splitting scheme. The resulting system of discrete equations is solved by a multigrid method. Numerical experiments are conducted to verify the practical stability and fourth-order accuracy of the proposed scheme. We also demonstrate that the compact scheme is more robust and efficient than the non-compact fourth-order scheme by applying to parallel computing and adaptive mesh refinement.
Original language | English |
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Pages (from-to) | 17-28 |
Number of pages | 12 |
Journal | Physica A: Statistical Mechanics and its Applications |
Volume | 409 |
DOIs | |
Publication status | Published - 2014 Sept 1 |
Bibliographical note
Funding Information:The corresponding author (J.S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2011-0023794 ). The authors thank the reviewers for the constructive and helpful comments on the revision of this article.
Keywords
- Adaptive mesh refinement
- Cahn-Hilliard equation
- Fourth-order compact scheme
- Multigrid
- Parallel computing
- Practically stable scheme
ASJC Scopus subject areas
- Statistics and Probability
- Condensed Matter Physics