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.
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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.