Open AccessSecond-order stabilized semi-implicit energy stable schemes for bubble assemblies in binary and ternary systems
Author(s) -
Hyun-Jung Choi,
Yanxiang Zhao
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021246
Subject(s) - discretization , fast fourier transform , mathematics , nonlinear system , ternary operation , binary number , collocation (remote sensing) , convergence (economics) , bubble , stability (learning theory) , rate of convergence , order (exchange) , fourier transform , mathematical analysis , physics , algorithm , computer science , arithmetic , mechanics , quantum mechanics , computer network , channel (broadcasting) , machine learning , economics , programming language , economic growth , finance
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.