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Controlling the accuracy of unconditionally stable algorithms in Cahn-Hilliard Equation

Mowei Cheng·James A. Warren
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Abstract

Given an unconditionally stable algorithm for solving the Cahn-Hilliard equation, we present a general calculation for an analytic time step $\d τ$ in terms of an algorithmic time step $\dt$. By studying the accumulative multi-step error in Fourier space and controlling the error with arbitrary accuracy, we determine an improved driving scheme $\dt=At^{2/3}$ and confirm the numerical results observed in a previous study \cite{Cheng1}.

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Mowei Cheng, James A. Warren. 2006-10-25. Controlling the accuracy of unconditionally stable algorithms in Cahn-Hilliard Equation. https://doi.org/10.1103/physreve.75.017702

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