Fast and accurate algorithms for simulating coarsening dynamics of Cahn–Hilliard equations

• Published in: Computational materials science Vol. 108; no. PB; pp. 272 - 282
• Main Authors: Ju, Lili, Zhang, Jian, Du, Qiang
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.10.2015; Elsevier
• Subjects: Cahn–Hilliard equation; Coarsening; Coarsening rate; Computation; Computer simulation; Dynamics; Fast Fourier transform; Materials science; Mathematical analysis; Mathematical models; Phase field model; Time integration; Variable mobility; Phase field model; Variable mobility; Cahn–Hilliard equation; Coarsening rate; Fast Fourier transform
• ISSN: 0927-0256; 1879-0801; 1879-0801
• DOI: 10.1016/j.commatsci.2015.04.046

[Display omitted] •A compact and exponential differences for solving Cahn-Hilliard equations.•Successful numerical predictions of coarsening kinetics of two phase mixtures.•Study of microstructure morphology, energy dissipation and coarsening rates. Numerical simulation of microstructure coarsening is a subject of great interest in computational materials science. The coarsening dynamics in a binary mixture can be modeled by the celebrated Cahn–Hilliard equations. To perform efficient and accurate long-time integrations, we develop a fast and stable high order numerical method for solving Cahn–Hilliard equations. The spatial discretization is carried out by the compact central difference scheme with FFT-based fast implementation while the time integration is done through the accurate exponential time differencing multistep approach. We demonstrate the effectiveness of the proposed method by numerical experiments and study computationally the coarsening kinetics corresponding to different choices of the diffusion mobility.