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

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

2006-09-14

arxiv.org/abs/cond-mat/0609354v2

Phys. Rev. E 75, 017702 (2007)

Physics

Condensed Matter

Materials Science

4 pages, latex

Scientific paper

10.1103/PhysRevE.75.017702

Given an unconditionally stable algorithm for solving the Cahn-Hilliard equation, we present a general calculation for an analytic time step $\d \tau$ 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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