Document Type
Article
Publication Date
8-27-2024
Abstract
The coupling between free and porous medium flows has received significant attention since it plays an important role in a wide range of problems from fluid-soil interactions to biofluid dynamics. However, modeling this coupled process remains a difficult task as it often involves a domain decomposition algorithm in conjunction with a special treatment at the interface. The problem can become more challenging under non-isothermal conditions because it requires the iterative procedure at every time step to simultaneously meet the transient mass continuity, force equilibrium, and energy balance for the entire system. This article presents a diffuse interface framework for modeling non-isothermal Stokes-Darcy flow and the corresponding finite element formulation that bypasses the need for explicitly splitting the domain into two, which enables the unified treatment for distinct regions with different hydrothermal flow regimes. To achieve this goal, we employ the Allen-Cahn type phase field model to generate the diffuse geometry, where the solution field can be seen as a regularized approximation of the Heaviside indicator function, allowing us to transfer the interface conditions into a set of immersed boundary conditions. Our formulation suggests that the isothermal operator splitting strategy can be adopted without compromising accuracy if the heat and mass transfer processes are decoupled by assuming that the density and viscosity of the phase constituents are independent to the temperature. Numerical examples are also introduced to verify the implementation and to demonstrate the model capacity.
Keywords
coupled Stokes-Darcy flow, diffuse interface, finite element method, heat transport, immersed boundary condition, phase field model
Language
English
Publication Title
International Journal for Numerical Methods in Engineering
Rights
© 2024 The Author(s). This is an open access work distributed under the terms of the Creative Commons Attribution-Non-Commercial (https://creativecommons.org/licenses/by-nc/4.0/) which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Recommended Citation
Suh HS. Diffuse interface modeling of non-isothermal Stokes-Darcy flow with immersed transmissibility conditions. Int J Numer Methods Eng. 2024; 125(24):e7589. doi: 10.1002/nme.7589
Manuscript Version
Final Publisher Version