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Accuracy of Unconditionally Stable Algorithms in Cahn-Hilliard Systems

Published

Author(s)

Mowei Cheng, James A. Warren

Abstract

Given an unconditionally stable algorithm for solving the Cahn-Hilliard equations, we provide the mathematical basis for arbitrary accuracy -- we present a general calculation for an analytical time step Δ Tau in terms of an algorithmic time step Δ Tau. By studying the accumulative multi-step error in Fourier space and controlling the error with arbitrary accuracy, we determine an improved driving scheme Δ Tau = A Tau 2/3 and confirm the numerical results observed in a previous study [5].
Citation
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Volume
75
Issue
1

Keywords

Cahn-Hilliard equation, unconditional stabilities

Citation

Cheng, M. and Warren, J. (2007), Accuracy of Unconditionally Stable Algorithms in Cahn-Hilliard Systems, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) (Accessed April 12, 2024)
Created January 11, 2007, Updated June 2, 2021