Abstract
To study natural convection problems in two-phase flows, a non-isothermal two-phase flow model incorporating differential viscosities and thermal diffusivities is considered and analyzed via the phase-field method. This modeling framework involves the Multiphysics coupling of the Cahn-Hilliard phase field equations, heat transfer equation, and Navier-Stokes equations, resulting in a strongly nonlinear system. To efficiently solve the sophisticated system, we develop, analyze, and demonstrate a decoupled linear fully discrete scheme, which leverages the invariant energy quadratization strategy for the Cahn-Hilliard phase field system, the artificial compressibility method without artificial pressure boundary condition, an explicit-implicit treatment of nonlinear terms, and the addition of several key stabilization terms. This scheme is proven uniquely solvable per time step and unconditionally stable. A range of 2D and 3D numerical simulations, including accuracy tests, stability tests, interface pinch off, one or two non-isothermal air bubbles rising, Rayleigh-Taylor instability, and thermal plumes, are carried out to illustrate the model and algorithm's features and broad applicability.
Recommended Citation
J. Li et al., "A Fully Discrete Decoupled Scheme and Applications for Non-isothermal Two-phase Flow Model with Different Viscosities and Thermal Diffusivities," Computer Methods in Applied Mechanics and Engineering, vol. 451, article no. 118669, Elsevier, Apr 2026.
The definitive version is available at https://doi.org/10.1016/j.cma.2025.118669
Department(s)
Mathematics and Statistics
Publication Status
Full Text Access
Keywords and Phrases
Artificial compressibility method; Invariant energy quadratization method; Natural convection,; Unconditional energy stability
International Standard Serial Number (ISSN)
0045-7825
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 Elsevier, All rights reserved.
Publication Date
01 Apr 2026
