Fast and stable explicit operator splitting methods for phase-field models

JOURNAL OF COMPUTATIONAL PHYSICS

卷:303

Article

Cheng, Yuanzhen¹  Kurganov, Alexander¹  Qu, Zhuolin¹  Tang, Tao² 

[1] Tulane Univ, Dept Math, New Orleans, LA 70118 USA

[2] Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China

关键词: Phase-field models;    Molecular beam epitaxy equation;    Cahn-Hilliard equation;    Operator splitting methods;    Semi-discrete finite-difference schemes;    Large stability domain explicit Runge-Kutta methods;    Pseudo-spectral methods;    Adaptive time-stepping;   

DOI  :  10.1016/j.jcp.2015.09.005

来源: Elsevier

【 摘 要 】

Numerical simulations of phase-field models require long time computations and therefore it is necessary to develop efficient and highly accurate numerical methods. In this paper, we propose fast and stable explicit operator splitting methods for both one- and two-dimensional nonlinear diffusion equations for thin film epitaxy with slope selection and the Cahn-Hilliard equation. The equations are split into nonlinear and linear parts. The nonlinear part is solved using a method of lines together with an efficient large stability domain explicit ODE solver. The linear part is solved by a pseudo-spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size. We demonstrate the performance of the proposed methods on a number of one- and two-dimensional numerical examples, where different stages of coarsening such as the initial preparation, alternating rapid structural transition and slow motion can be clearly observed. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free