Abstract
We analyze the effective time step size of a nonlinear convex splitting scheme for the Cahn–Hilliard (CH) equation. The convex splitting scheme is unconditionally stable, which implies we can use arbitrary large time-steps and get stable numerical solutions. However, if we use a too large time-step, then we have not only discretization error but also time-step rescaling problem. In this paper, we show the time-step rescaling problem from the convex splitting scheme by comparing with a fully implicit scheme for the CH equation. We perform various test problems. The computation results confirm the time-step rescaling problem and suggest that we need to use small enough time-step sizes for the accurate computational results.
Original language | English |
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Pages (from-to) | 448-460 |
Number of pages | 13 |
Journal | Comunicata Scientiae |
Volume | 25 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2019 Feb |
Keywords
- Cahn–Hilliard equation
- Convex splitting
- Effective time step
- Fourier analysis
ASJC Scopus subject areas
- Agricultural and Biological Sciences(all)