Effective Time Step Analysis of a Nonlinear Convex Splitting Scheme for the Cahn–Hilliard Equation

Effective Time Step Analysis of a Nonlinear Convex Splitting Scheme for the Cahn–Hilliard Equation

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.