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Volume 27, Issue 4
Decoupled, Energy Stable Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Logarithmic Flory-Huggins Potential

Hong-En Jia, Ya-Yu Guo, Ming Li, Yunqing Huang & Guo-Rui Feng

DOI: 10.4208/cicp.OA-2019-0034

Commun. Comput. Phys., 27 (2020), pp. 1053-1075.

Published online: 2020-02

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  • Abstract

In this paper, a decoupling numerical method for solving Cahn-Hilliard-Hele-Shaw system with logarithmic potential is proposed. Combing with a convex-splitting of the energy functional, the discretization of the Cahn-Hilliard equation in time is presented. The nonlinear term in Cahn-Hilliard equation is decoupled from the pressure gradient by using a fractional step method. Therefore, to update the pressure, we just need to solve a Possion equation at each time step by using an incremental pressure-correction technique for the pressure gradient in Darcy equation. For logarithmic potential, we use the regularization procedure, which make the domain for the regularized functional $F$($ф$) is extended from (−1,1) to (−∞,∞). Further, the stability and the error estimate of the proposed method are proved. Finally, a series of numerical experiments are implemented to illustrate the theoretical analysis.

  • Keywords

Logarithmic potential, Cahn-Hilliard-Hele-Shaw, decoupling.

  • AMS Subject Headings

35Q30, 74S05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jiahongen@aliyun.com (Hong-En Jia)

903708742@qq.com (Ya-Yu Guo)

liming04@gmail.com (Ming Li)

huangyq@xtu.edu.cn (Yunqing Huang)

fguorui@163.com (Guo-Rui Feng)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-1053, author = {Jia , Hong-EnGuo , Ya-YuLi , MingHuang , Yunqing and Feng , Guo-Rui}, title = {Decoupled, Energy Stable Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Logarithmic Flory-Huggins Potential}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {4}, pages = {1053--1075}, abstract = {

In this paper, a decoupling numerical method for solving Cahn-Hilliard-Hele-Shaw system with logarithmic potential is proposed. Combing with a convex-splitting of the energy functional, the discretization of the Cahn-Hilliard equation in time is presented. The nonlinear term in Cahn-Hilliard equation is decoupled from the pressure gradient by using a fractional step method. Therefore, to update the pressure, we just need to solve a Possion equation at each time step by using an incremental pressure-correction technique for the pressure gradient in Darcy equation. For logarithmic potential, we use the regularization procedure, which make the domain for the regularized functional $F$($ф$) is extended from (−1,1) to (−∞,∞). Further, the stability and the error estimate of the proposed method are proved. Finally, a series of numerical experiments are implemented to illustrate the theoretical analysis.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0034}, url = {http://global-sci.org/intro/article_detail/cicp/14826.html} }
TY - JOUR T1 - Decoupled, Energy Stable Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Logarithmic Flory-Huggins Potential AU - Jia , Hong-En AU - Guo , Ya-Yu AU - Li , Ming AU - Huang , Yunqing AU - Feng , Guo-Rui JO - Communications in Computational Physics VL - 4 SP - 1053 EP - 1075 PY - 2020 DA - 2020/02 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2019-0034 UR - https://global-sci.org/intro/article_detail/cicp/14826.html KW - Logarithmic potential, Cahn-Hilliard-Hele-Shaw, decoupling. AB -

In this paper, a decoupling numerical method for solving Cahn-Hilliard-Hele-Shaw system with logarithmic potential is proposed. Combing with a convex-splitting of the energy functional, the discretization of the Cahn-Hilliard equation in time is presented. The nonlinear term in Cahn-Hilliard equation is decoupled from the pressure gradient by using a fractional step method. Therefore, to update the pressure, we just need to solve a Possion equation at each time step by using an incremental pressure-correction technique for the pressure gradient in Darcy equation. For logarithmic potential, we use the regularization procedure, which make the domain for the regularized functional $F$($ф$) is extended from (−1,1) to (−∞,∞). Further, the stability and the error estimate of the proposed method are proved. Finally, a series of numerical experiments are implemented to illustrate the theoretical analysis.

Jia , Hong-EnGuo , Ya-YuLi , MingHuang , Yunqing and Feng , Guo-Rui. (2020). Decoupled, Energy Stable Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Logarithmic Flory-Huggins Potential. Communications in Computational Physics. 27 (4). 1053-1075. doi:10.4208/cicp.OA-2019-0034
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