4.6 Article

Energy Stable Semi-implicit Schemes for Allen-Cahn-Ohta-Kawasaki Model in Binary System

期刊

JOURNAL OF SCIENTIFIC COMPUTING
卷 80, 期 3, 页码 1656-1680

出版社

SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-019-00993-4

关键词

Ohta-Kawasaki model; Energy stability; Penalty method; Fourier collocation; Bubble assembly

资金

  1. Columbian College Facilitating Funds (CCFF 2018) of George Washington University
  2. Simons Foundation [357963]

向作者/读者索取更多资源

In this paper, we propose a first order energy stable linear semi-implicit method for solving the Allen-Cahn-Ohta-Kawasaki equation. By introducing a new nonlinear term in the Ohta-Kawasaki free energy functional, all the system forces in the dynamics are localized near the interfaces which results in the desired hyperbolic tangent profile. In our numerical method, the time discretization is done by some stabilization technique in which some extra nonlocal but linear term is introduced and treated explicitly together with other linear terms, while other nonlinear and nonlocal terms are treated implicitly. The spatial discretization is performed by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are proved for this method in both semi-discretization and full discretization levels. Numerical experiments indicate the force localization and desire hyperbolic tangent profile due to the new nonlinear term. We test the first order temporal convergence rate of the proposed scheme. We also present hexagonal bubble assembly as one type of equilibrium for the Ohta-Kawasaki model. Additionally, the two-third law between the number of bubbles and the strength of long-range interaction is verified which agrees with the theoretical studies.

作者

我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。

评论

主要评分

4.6
评分不足

次要评分

新颖性
-
重要性
-
科学严谨性
-
评价这篇论文

推荐

暂无数据
暂无数据