具有浸入式渗透条件的非等温斯托克斯-达西流的扩散界面建模

IF 2.7 3区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY International Journal for Numerical Methods in Engineering Pub Date : 2024-08-28 DOI:10.1002/nme.7589
Hyoung Suk Suh
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引用次数: 0

摘要

自由介质流与多孔介质流之间的耦合受到了广泛关注,因为它在从流体-土壤相互作用到生物流体动力学等一系列问题中发挥着重要作用。然而,对这一耦合过程进行建模仍然是一项艰巨的任务,因为它通常涉及到域分解算法以及界面的特殊处理。在非等温条件下,这个问题会变得更具挑战性,因为它要求在每个时间步长上的迭代程序同时满足整个系统的瞬态质量连续性、力平衡和能量平衡。本文提出了一种用于模拟非等温斯托克斯-达西流的扩散界面框架以及相应的有限元计算方法,该方法绕过了明确地将领域一分为二的需要,从而能够统一处理具有不同热液流态的不同区域。为实现这一目标,我们采用 Allen-Cahn 型相场模型来生成扩散几何,其中的解场可视为 Heaviside 指标函数的正则化近似值,使我们能够将界面条件转换为一组沉浸边界条件。我们的计算方法表明,如果假定相成分的密度和粘度与温度无关,将传热和传质过程解耦,就可以采用等温算子拆分策略,而不会影响精度。此外,还介绍了一些数值示例,以验证模型的实现并展示模型的能力。
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Diffuse interface modeling of non‐isothermal Stokes‐Darcy flow with immersed transmissibility conditions
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.
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来源期刊
CiteScore
5.70
自引率
6.90%
发文量
276
审稿时长
5.3 months
期刊介绍: The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems. The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.
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