A Second-Order, Mass-Conservative, Unconditionally Stable and Bound-Preserving Finite Element Method for the Quasi-Incompressible Cahn-Hilliard-Darcy System
Abstract
A second-order numerical method is developed for solving the quasi-incompressible Cahn-Hilliard-Darcy system with the Flory-Huggins potential for two immiscible fluids of variable densities and viscosities in a porous medium or a Hele-Shaw cell. We show that the scheme is uniquely solvable, mass-conservative, bound-preserving and unconditionally energy stable. The key for bound-preserving is the utilization of second order convex-concave splitting of the logarithmic potential, and the discrete L1 estimate of the singular potential. Ample numerical tests are reported to validate the accuracy and robustness of the proposed numerical scheme.
Recommended Citation
Y. Gao et al., "A Second-Order, Mass-Conservative, Unconditionally Stable and Bound-Preserving Finite Element Method for the Quasi-Incompressible Cahn-Hilliard-Darcy System," Journal of Computational Physics, vol. 518, article no. 113340, Elsevier, Dec 2024.
The definitive version is available at https://doi.org/10.1016/j.jcp.2024.113340
Department(s)
Mathematics and Statistics
Keywords and Phrases
Bound-preserving; Cahn-Hilliard-Darcy; Energy stability; Quasi-incompressible; Second order accuracy; Variable density
International Standard Serial Number (ISSN)
1090-2716; 0021-9991
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Elsevier, All rights reserved.
Publication Date
01 Dec 2024
Comments
Basic and Applied Basic Research Foundation of Guangdong Province, Grant 12271237