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.
翻译:在目前的工作中,我们提出了多阶段和多部分不压缩流动的一致和保守模式,其中可能存在任意的阶段和组成部分数目。每个阶段都有一种背景流体,称为纯阶段,每个阶段都是不相容的,每个阶段是分不解的。该模式是根据多阶段阶段-实地模式开发的,其中包括接触角边界条件、分散的域法,以及对多阶段和多部分流动的拟议一致性条件的分析。该模式保存了单个纯阶段的质量、每个组成部分在可溶性区域的数量,从而保存了液体混合物的质量,以及流动的势头。该模式确保了不产生任何虚构的阶段或组成部分,而分阶段模型的体积部分的相加是团结的,因此没有地方空隙或填充量过多。该模式满足了物理能源法,并且是加利利平面和多部分流动。该模式为拟议模式制定了一个相应的数字计划,其形式准确性在时间和空间上都是2个顺序,因此流动的液体质量和流动性混合,以及流动的动力动力动力动力。该模式可以确保产生任何虚构的阶段性或动态。该模式的稳定性和稳定性,并展示了多阶段性模式,以维护高层次试验。该模式。