A Decoupled, Linear, Unconditionally Stable, and Fully Discrete Finite Element Scheme for Two-phase Ferrofluid Flows with Different Densities and Viscosities
Abstract
In this paper, a model describing the behavior of two-phase ferrofluid flows with different densities and viscosities is established by using phase field techniques. This model is a coupled nonlinear multiphysics PDE system consisting of Cahn-Hilliard equations, Navier-Stokes equations, magnetization equation and magnetostatic equation. By reformulating the magnetic potential equation, applying the artificial compressibility method, utilizing the implicit-explicit scheme for treating the nonlinear terms, and adding several stabilization terms, we propose a linear, decoupled and fully discrete finite element method approximation for the established model. And it is strictly proved to be unconditionally stable and uniquely solvable at each time step. Furthermore, the proposed scheme does not impose any artificial boundary conditions on the pressure. In order to accurately capture the diffuse interface in the numerical simulation, we also apply the adaptive mesh strategy to locally refine the mesh around the interfacial region. Several informative numerical experiments, including an accuracy test, deformation of a ferrofluid droplet, one or two air bubbles rising in ferrofluids, a controllable ferrofluid droplet in a Y-shape domain, and the Rosensweig instability under uniformly or nonuniformly applied magnetic field, are performed to illustrate various features of the proposed model and scheme, especially their applicability for the cases of high density ratio and high viscosity ratio.
Recommended Citation
X. Chen et al., "A Decoupled, Linear, Unconditionally Stable, and Fully Discrete Finite Element Scheme for Two-phase Ferrofluid Flows with Different Densities and Viscosities," Journal of Computational Physics, vol. 539, article no. 114209, Elsevier, Oct 2025.
The definitive version is available at https://doi.org/10.1016/j.jcp.2025.114209
Department(s)
Mathematics and Statistics
Keywords and Phrases
Artificial compressibility; Different densities; Different viscosities; Phase field; Two-phase ferrohydrodynamics
International Standard Serial Number (ISSN)
1090-2716; 0021-9991
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2025 Elsevier, All rights reserved.
Publication Date
15 Oct 2025
Comments
Natural Science Foundation of Shaanxi Province, Grant 12471408