A consistent and conservative model and its scheme for N-phase-M-component incompressible flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:434

Article

Huang, Ziyang¹  Lin, Guang^1,2  Ardekani, Arezoo M.¹ 

[1] Purdue Univ, Sch Mech Engn, W Lafayette, IN 47907 USA

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

关键词: Multi-phase;    Multi-component;    Phase-Field model;    Diffuse domain approach;    Consistent scheme;    Conservative scheme;   

DOI  :  10.1016/j.jcp.2021.110229

来源: Elsevier

【 摘 要 】

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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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