Decoupled Energy-Law Preserving Numerical Schemes for the Cahn-Hilliard-Darcy System
We study two novel decoupled energy-law preserving and mass-conservative numerical schemes for solving the Cahn-Hilliard-Darcy system which models two-phase flow in porous medium or in a Hele-Shaw cell. In the first scheme, the velocity in the Cahn-Hilliard equation is treated explicitly so that the Darcy equation is completely decoupled from the Cahn-Hilliard equation. In the second scheme, an intermediate velocity is used in the Cahn-Hilliard equation which allows for the decoupling. We show that the first scheme preserves a discrete energy law with a time-step constraint, while the second scheme satisfies an energy law without any constraint and is unconditionally stable. Ample numerical experiments are performed to gauge the efficiency and robustness of our scheme.
D. Han and X. Wang, "Decoupled Energy-Law Preserving Numerical Schemes for the Cahn-Hilliard-Darcy System," Numerical Methods for Partial Differential Equations, vol. 32, no. 3, pp. 936-954, John Wiley & Sons, May 2016.
The definitive version is available at https://doi.org/10.1002/num.22036
Mathematics and Statistics
Keywords and Phrases
Convergence of numerical methods; Flow of fluids; Porous materials; Cahn-Hilliard-Darcy; convex-splitting; decoupling; energy-law; Hele-Shaw cells; Long time stabilities; Porous medium; Two phase flow; Long-time stability; Stability; Two-phase flow
International Standard Serial Number (ISSN)
Article - Journal
© 2016 John Wiley & Sons, All rights reserved.
01 May 2016