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 December 14, 2024)
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Accuracy of Unconditionally Stable Algorithms in Cahn-Hilliard Systems
Published
Author(s)
,
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
Pub Type
Journals
Keywords
Cahn-Hilliard equation, unconditional stabilities
Citation
Issues
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Created January 11, 2007, Updated June 2, 2021