An Efficient and Unconditionally Energy Stable Fully Discrete Scheme for the Confined Ternary Blended Polymers Model
Year: 2022
Author: Guanghua Ji, Zhen Xu, Yuqi Yang
CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 3 : pp. 480–514
Abstract
In this paper, we develop a fully discrete scheme to solve the confined ternary blended polymers (TBP) model with four order parameters based on the stabilized-scalar auxiliary variable (S-SAV) approach in time and the Fourier spectral method in space. Then, theoretical analysis is given for the scheme based on the backward differentiation formula. The unconditional energy stability and mass conservation are derived. Rigorous error analysis is carried out to show that the fully discrete scheme converges with order $\mathcal{O}(\tau^2+h^m)$ in the sense of the $L^2$ norm, where $\tau$ is the time step, $h$ is the spatial step, and $m$ is the regularity of the exact solution. Finally, some numerical results are given to demonstrate the theoretical analysis. Moreover, the phase separation of two kinds of polymer particles, namely, Ashura and Janus core-shell particles, is presented to show the morphological structures.
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/csiam-am.SO-2021-0036
CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 3 : pp. 480–514
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Confinement ternary blended polymers unconditional energy stability error estimates Fourier spectral method.