Abstract
We propose a new diffuse interface model for two-phase porous media ferrofluid flows, employing the phase-field method and establishing an associated energy law. This thermodynamically consistent multi-physics model integrates the Cahn-Hilliard equations, Darcy equations, the magnetostatic equation, and magnetization equations. To efficiently solve the system by addressing its inherent nonlinearities, coupling, and saddle-point structure, we incorporate several advanced techniques, including the SAV-ZEC method to handle nonlinearities and couplings, a reformulated approach to decouple the linear coupling of the magnetic potential and magnetization, and the pressure projection method to decouple velocity and pressure. This results in a numerical scheme that is linear, fully decoupled, second-order accurate in time, and unconditionally energy stable, effectively transforming the complex system into a series of elliptic problems. Compared with the existing works for the two-phase free ferrofluid flows, one major difficulty for both the modeling and algorithm development in this work arises from the different function space used for the Darcy equation, which is addressed by several novel techniques. We also prove the unconditional energy stability and unique solvability of the scheme. Through a series of 2D and 3D numerical experiments, we verify the stability and accuracy of the proposed scheme and then demonstrate the model's ability to capture fundamental phenomenological features of two-phase porous ferrofluids, such as the Saffman-Taylor fingering instability.
Recommended Citation
G. D. Zhang et al., "A Diffuse Interface Model and Fully Decoupled, Energy-stable Scheme for the Two-phase Ferrofluid Flows in Porous Media," Journal of Computational Physics, vol. 548, article no. 114561, Elsevier, Mar 2026.
The definitive version is available at https://doi.org/10.1016/j.jcp.2025.114561
Department(s)
Mathematics and Statistics
Publication Status
Open Access
Keywords and Phrases
Decoupling; Ferrofluid; Fingering instability; Porous media; SAV-ZEC; Stability
International Standard Serial Number (ISSN)
1090-2716; 0021-9991
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 Elsevier, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 Mar 2026
