- Volume 17 Issue 3
DOI QR Code
COMPARISON OF DIFFERENT NUMERICAL SCHEMES FOR THE CAHN-HILLIARD EQUATION
- Lee, Seunggyu (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY) ;
- Lee, Chaeyoung (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY) ;
- Lee, Hyun Geun (INSTITUTE OF MATHEMATICAL SCIENCES, EWHA W. UNIVERSITY) ;
- Kim, Junseok (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
- Received : 2013.06.08
- Accepted : 2013.07.01
- Published : 2013.09.25
The Cahn-Hilliard equation was proposed as a phenomenological model for describing the process of phase separation of a binary alloy. The equation has been applied to many physical applications such as amorphological instability caused by elastic non-equilibrium, image inpainting, two- and three-phase fluid flow, phase separation, flow visualization and the formation of the quantum dots. To solve the Cahn-Hillard equation, many numerical methods have been proposed such as the explicit Euler's, the implicit Euler's, the Crank-Nicolson, the semi-implicit Euler's, the linearly stabilized splitting and the non-linearly stabilized splitting schemes. In this paper, we investigate each scheme in finite-difference schemes by comparing their performances, especially stability and efficiency. Except the explicit Euler's method, we use the fast solver which is called a multigrid method. Our numerical investigation shows that the linearly stabilized stabilized splitting scheme is not unconditionally gradient stable in time unlike the known result. And the Crank-Nicolson scheme is accurate but unstable in time, whereas the non-linearly stabilized splitting scheme has advantage over other schemes on the time step restriction.
Supported by : National Research Foundation of Korea(NRF)
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