@Article{CiCP-27-4,
author = {Jia, Hong-En and Ya-Yu, Guo and Ming, Li and Yunqing, Huang and Guo-Rui, Feng},
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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2019-0034},
url = {https://global-sci.com/article/79792/decoupled-energy-stable-numerical-scheme-for-the-cahn-hilliard-hele-shaw-system-with-logarithmic-flory-huggins-potential}
}