Year: 2019
Communications in Computational Physics, Vol. 25 (2019), Iss. 2 : pp. 448–460
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2017-0260
Communications in Computational Physics, Vol. 25 (2019), Iss. 2 : pp. 448–460
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Cahn–Hilliard equation convex splitting effective time step Fourier analysis.