Volume 14, Issue 1
A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations

Shuang Geng, Tongmao Li, Qiongwei Ye & Xiaofeng Yang

Adv. Appl. Math. Mech., 14 (2022), pp. 101-124.

Published online: 2021-11

Preview Full PDF 102 4174
Export citation
  • 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.

  • Keywords

Phase-field, Diblock copolymer, Allen-Cahn, nonlocal, second order, unconditional energy stability.

  • AMS Subject Headings

65N12, 65P40, 65Z05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-14-101, author = {Geng , Shuang and Li , Tongmao and Ye , Qiongwei and Yang , Xiaofeng}, title = {A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {14}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0293}, url = {http://global-sci.org/intro/article_detail/aamm/19978.html} }
TY - JOUR T1 - A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations AU - Geng , Shuang AU - Li , Tongmao AU - Ye , Qiongwei AU - Yang , Xiaofeng JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 101 EP - 124 PY - 2021 DA - 2021/11 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2020-0293 UR - https://global-sci.org/intro/article_detail/aamm/19978.html KW - Phase-field, Diblock copolymer, Allen-Cahn, nonlocal, second order, unconditional energy stability. AB -

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.

Shuang Geng, Tongmao Li, Qiongwei Ye & Xiaofeng Yang. (1970). A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations. Advances in Applied Mathematics and Mechanics. 14 (1). 101-124. doi:10.4208/aamm.OA-2020-0293
Copy to clipboard
The citation has been copied to your clipboard