Second-order stabilized semi-implicit energy stable schemes for bubble assemblies in binary and ternary systems
Second-order stabilized semi-implicit energy stable schemes for bubble assemblies in binary and ternary systems
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DOI：
10.3934/dcdsb.2021246
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
H. Choi;Yanxiang Zhao
中科院分区：
文献类型：
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作者：
H. Choi;Yanxiang Zhao
本文提出了求解Allen-Cahn-Ohta-Kawasaki方程和Allen-Cahn-Ohta-Nakazawa方程的二阶稳定化半隐式方法。在数值方法中，一些非局部线性稳定化项被引入并与其他线性项隐式处理，而其他非线性和非局部项被显式处理。我们考虑两种不同形式的这种稳定剂，并比较关于能量稳定性的差异。空间离散化由基于FFT的快速实现的傅里叶配置法进行。数值上，我们验证了所提出的方案的二阶时间收敛速度。在二元和三元体系中，粗化动力学被可视化为六边形或正方形图案的气泡组件。
In this paper, we propose some second-order stabilized semi-implicit methods for solving the Allen-Cahn-Ohta-Kawasaki and the Allen-Cahn-Ohta-Nakazawa equations. In the numerical methods, some nonlocal linear stabilizing terms are introduced and treated implicitly with other linear terms, while other nonlinear and nonlocal terms are treated explicitly. We consider two different forms of such stabilizers and compare the difference regarding the energy stability. The spatial discretization is performed by the Fourier collocation method with FFT-based fast implementations. Numerically, we verify the second order temporal convergence rate of the proposed schemes. In both binary and ternary systems, the coarsening dynamics is visualized as bubble assemblies in hexagonal or square patterns.