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A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations

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.

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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

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