A parallel domain decomposition-based implicit method for the Cahn-Hilliard-Cook phase-field equation in 3D

JOURNAL OF COMPUTATIONAL PHYSICS

卷:285

Article

Zheng, Xiang¹  Yang, Chao^2,5  Cai, Xiao-Chuan³  Keyes, David^1,4 

[1] Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USA

[2] Chinese Acad Sci, Inst Software, Beijing 100190, Peoples R China

[3] Univ Colorado, Dept Comp Sci, Boulder, CO 80309 USA

[4] King Abdullah Univ Sci & Technol, Thuwal 23955, Saudi Arabia

[5] Chinese Acad Sci, State Key Lab Comp Sci, Beijing 100190, Peoples R China

关键词: Cahn-Hilliard-Cook;    Thermal fluctuation;    Implicit method;    Newton-Krylov-Schwarz;    Parallel scalability;    Steady state solutions;   

DOI  :  10.1016/j.jcp.2015.01.016

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free