Decoupled, Energy Stable Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Logarithmic Flory-Huggins Potential
Year: 2020
Author: Hong-En Jia, Ya-Yu Guo, Ming Li, Yunqing Huang, Guo-Rui Feng
Communications in Computational Physics, Vol. 27 (2020), Iss. 4 : pp. 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.
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/cicp.OA-2019-0034
Communications in Computational Physics, Vol. 27 (2020), Iss. 4 : pp. 1053–1075
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Logarithmic potential Cahn-Hilliard-Hele-Shaw decoupling.
Author Details
-
An explicit conservative Saul’yev scheme for the Cahn–Hilliard equation
Yang, Junxiang
Li, Yibao
Lee, Chaeyoung
Lee, Hyun Geun
Kwak, Soobin
Hwang, Youngjin
Xin, Xuan
Kim, Junseok
International Journal of Mechanical Sciences, Vol. 217 (2022), Iss. P.106985
https://doi.org/10.1016/j.ijmecsci.2021.106985 [Citations: 12]