Abstract
This work extends the previous two-dimensional compact scheme for the Cahn-Hilliard equation (Lee et al., 2014) to three-dimensional space. The proposed scheme, derived by combining a compact formula and a linearly stabilized splitting scheme, has second-order accuracy in time and fourth-order accuracy in space. The discrete system is conservative and practically stable. We also implement the compact scheme in a three-dimensional adaptive mesh refinement framework. The resulting system of discrete equations is solved by using a multigrid. We demonstrate the performance of our proposed algorithm by several numerical experiments.
Original language | English |
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Pages (from-to) | 108-116 |
Number of pages | 9 |
Journal | Computer Physics Communications |
Volume | 200 |
DOIs | |
State | Published - 1 Mar 2016 |
Keywords
- Adaptive mesh refinement
- Cahn-Hilliard equation
- Finite difference method
- Fourth-order compact scheme
- Multigrid