A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations
Year: 2022
Author: Shuang Geng, Tongmao Li, Qiongwei Ye, Xiaofeng Yang
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 1 : pp. 101–124
Abstract
We develop a new conservative Allen-Cahn phase-field model for diblock copolymers in this paper by using the Allen-Cahn type gradient flow approach for the classical Ohta-Kawaski free energy. The change in volume fraction of two composing monomers is eliminated by using a nonlocal Lagrange multiplier. Based on the recently developed stabilized Scalar Auxiliary Variable method, we have further developed an effective numerical scheme to solve the model. The scheme is highly efficient and only two linear and decoupled equations are needed to solve at every time step. We then prove that the numerical method is unconditionally energy stable, the stability and accuracy of the new scheme are demonstrated by numerous numerical examples conducted. By qualitatively comparing the equilibrium solution obtained by the new model and the classic Cahn-Hilliard model, we illustrate the effectiveness of the new model.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0293
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 1 : pp. 101–124
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Phase-field Diblock copolymer Allen-Cahn nonlocal second order unconditional energy stability.
Author Details
Shuang Geng Email
Tongmao Li Email
Qiongwei Ye Email
Xiaofeng Yang Email
-
A new Allen–Cahn type two-model phase-field crystal model for fcc ordering and its numerical approximation
Li, Qi | Cui, Ning | Zheng, Supei | Mei, LiquanApplied Mathematics Letters, Vol. 132 (2022), Iss. P.108211
https://doi.org/10.1016/j.aml.2022.108211 [Citations: 11] -
Large time-stepping, delay-free, and invariant-set-preserving integrators for the viscous Cahn–Hilliard–Oono equation
Zhang, Hong | Liu, Lele | Qian, Xu | Song, SongheJournal of Computational Physics, Vol. 499 (2024), Iss. P.112708
https://doi.org/10.1016/j.jcp.2023.112708 [Citations: 1] -
Low Regularity Integrators for the Conservative Allen–Cahn Equation with a Nonlocal Constraint
Doan, Cao-Kha | Hoang, Thi-Thao-Phuong | Ju, LiliJournal of Scientific Computing, Vol. 101 (2024), Iss. 3
https://doi.org/10.1007/s10915-024-02703-1 [Citations: 0] -
A phase-field method for elastic mechanics with large deformation
Xu, Jiacheng | Hu, Dan | Zhou, HanJournal of Computational Physics, Vol. 471 (2022), Iss. P.111630
https://doi.org/10.1016/j.jcp.2022.111630 [Citations: 2] -
Fully discrete Spectral-Galerkin scheme for a ternary Allen–Cahn type mass-conserved Nakazawa–Ohta phase-field model for triblock copolymers
Wang, Ziqiang | Zhang, Jun | Yang, XiaofengJournal of Computational and Applied Mathematics, Vol. 419 (2023), Iss. P.114699
https://doi.org/10.1016/j.cam.2022.114699 [Citations: 2] -
Maximum principle preserving and unconditionally stable scheme for a conservative Allen–Cahn equation
Choi, Yongho | Kim, JunseokEngineering Analysis with Boundary Elements, Vol. 150 (2023), Iss. P.111
https://doi.org/10.1016/j.enganabound.2023.02.016 [Citations: 5] -
Decoupled, second-order accurate in time and unconditionally energy stable scheme for a hydrodynamically coupled ternary Cahn-Hilliard phase-field model of triblock copolymer melts
Wang, Ziqiang | Zhang, Jun | Yang, XiaofengComputers & Mathematics with Applications, Vol. 124 (2022), Iss. P.241
https://doi.org/10.1016/j.camwa.2022.08.046 [Citations: 0] -
Stability analysis for a maximum principle preserving explicit scheme of the Allen–Cahn equation
Ham, Seokjun | Kim, JunseokMathematics and Computers in Simulation, Vol. 207 (2023), Iss. P.453
https://doi.org/10.1016/j.matcom.2023.01.016 [Citations: 14]