An Efficient and Unconditionally Energy Stable Fully Discrete Scheme for the Confined Ternary Blended Polymers Model

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.

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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.

Author Details

Guanghua Ji

Zhen Xu

Yuqi Yang