Fast and accurate coarsening simulation with an unconditionally stable time step

Benjamin P. Vollmayr-Lee and Andrew D. Rutenberg
Phys. Rev. E 68, 066703 – Published 23 December 2003
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Abstract

We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that are unconditionally stable and so provide significantly faster accuracy-controlled simulation. Our stability analysis is based on Eyre’s theorem and unconditional von Neumann stability analysis, both of which we present. Numerical tests confirm the accuracy of the von Neumann approach, which is straightforward and should be widely applicable in phase-field modeling. For the Cahn-Hilliard case, we show that accuracy can be controlled with an unbounded time step Δt that grows with time t as Δttα. We develop a classification scheme for the step exponent α and demonstrate that a class of simple linear algorithms gives α=1/3. For this class the speedup relative to a fixed time step grows with N, the linear size of the system, as N/lnN. With conservative choices for the parameters controlling accuracy and finite-size effects we find that an 81922 lattice can be integrated 300 times faster than with the Euler method.

  • Received 8 August 2003

DOI:https://doi.org/10.1103/PhysRevE.68.066703

©2003 American Physical Society

Authors & Affiliations

Benjamin P. Vollmayr-Lee*

  • Department of Physics, Bucknell University, Lewisburg, Pennsylvania 17837, USA

Andrew D. Rutenberg

  • Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5

  • *Electronic address: bvollmay@bucknell.edu
  • Electronic address: andrew.rutenberg@dal.ca; URL: http://www.physics.dal.ca/adr

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Vol. 68, Iss. 6 — December 2003

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