A parallel domain decomposition-based implicit method for the Cahn-Hilliard-Cook phase-field equation in 3D
X. Zheng, C. Yang, X.-C. Cai, and D. Keyes
Journal of Computational Physics, 285, pp. 55-70, (2015)
Keywords
CahnHilliardCook, Thermal fluctuation, Implicit method, NewtonKrylovSchwarz, Parallel scalability, Steady state solutions
Abstract
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We present a numerical algorithm for simulating the spinodal
decomposition described by the three dimensional Cahn–Hilliard–Cook
(CHC) equation, which is a fourth-order stochastic partial differential
equation with a noise term. The equation is discretized in space and
time based on a fully implicit, cell-centered finite difference scheme,
with an adaptive time-stepping strategy designed to accelerate the
progress to equilibrium. At each time step, a parallel
Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system.
We discuss various numerical and computational challenges associated
with the method. The numerical scheme is validated by a comparison with
an explicit scheme of high accuracy (and unreasonably high cost). We
present steady state solutions of the CHC equation in two and three
dimensions. The effect of the thermal fluctuation on the spinodal
decomposition process is studied. We show that the existence of the
thermal fluctuation accelerates the spinodal decomposition process and
that the final steady morphology is sensitive to the stochastic noise.
We also show the evolution of the energies and statistical moments. In
terms of the parallel performance, it is found that the implicit domain
decomposition approach scales well on supercomputers with a large number
of processors.
Code
DOI: 10.1016/j.jcp.2015.01.016
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