A consistent and conservative model and its scheme for N-phase-M-component incompressible flows
A consistent and conservative model and its scheme for N-phase-M-component incompressible flows
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DOI：
10.1016/j.jcp.2021.110229
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
Ziyang Huang;G. Lin;A. Ardekani
中科院分区：
文献类型：
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作者：
Ziyang Huang;G. Lin;A. Ardekani
在本工作中，我们提出了一个一致且保守的多相和多组分不可压缩流模型，其中可以有任意数量的相和组分。每个相都有一个背景流体，称为纯相，每对相是不混溶的，并且组分可溶解在某些特定相中。该模型是基于多相流相场模型，包括接触角边界条件，扩散域的方法，和建议的多相和多组分流的一致性条件的分析。该模型保留了单个纯相的质量、其可溶解区域中每种组分的量，从而保留了流体混合物的质量和流动的动量。它确保不会产生虚拟的相或组分，并且相场模型的体积分数之和在任何地方都是统一的，因此不会出现局部空隙或过度填充。它满足一个物理能量定律，并且是伽利略不变量。针对该模型建立了相应的数值格式，其形式精度在时间和空间上均为二阶。它是一致的和保守的，它的解决方案被证明保持伽利略不变性和能量定律。数值试验表明，所提出的模型和格式是有效的和强大的研究各种具有挑战性的多相和多组分流动。
In the present work, we propose a consistent and conservative model for multiphase and multicomponent incompressible flows, where there can be arbitrary numbers of phases and components. Each phase has a background fluid called the pure phase, each pair of phases is immiscible, and components are dissolvable in some specific phases. The model is developed based on the multiphase Phase-Field model including the contact angle boundary condition, the diffuse domain approach, and the analyses on the proposed consistency conditions for multiphase and multicomponent flows. The model conserves the mass of individual pure phases, the amount of each component in its dissolvable region, and thus the mass of the fluid mixture, and the momentum of the flow. It ensures that no fictitious phases or components can be generated and that the summation of the volume fractions from the Phase-Field model is unity everywhere so that there is no local void or overfilling. It satisfies a physical energy law and it is Galilean invariant. A corresponding numerical scheme is developed for the proposed model, whose formal accuracy is 2nd-order in both time and space. It is shown to be consistent and conservative and its solution is demonstrated to preserve the Galilean invariance and energy law. Numerical tests indicate that the proposed model and scheme are effective and robust to study various challenging multiphase and multicomponent flows.