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.

在目前的工作中，我们为多相和多组分不可压缩流提出了一个一致且保守的模型，其中可以有任意数量的相和组分。每个相都有一个称为纯相的背景流体，每对相都是不溶混的，并且某些特定相中的组分是可溶的。该模型是在多相相场模型的基础上开发的，包括接触角边界条件，扩散域方法以及对所提出的多相和多组分流的一致性条件的分析。该模型保留了各个纯相的质量，可溶解区域中每种组分的量，从而节省了流体混合物的质量以及流动的动量。它确保不会生成虚拟的相或成分，并且确保“相场”模型中体积分数的总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。它满足物理能定律，并且是伽利略不变的。针对所提出的模型开发了相应的数值方案，其形式精度在时间和空间上均为二阶。它被证明是一致和保守的，其解决方案被证明可以保留伽利略不变性和能量定律。数值测试表明，所提出的模型和方案对于研究各种具有挑战性的多相和多组分流动是有效且稳健的。为所提出的模型开发了相应的数值方案，其形式精度在时间和空间上均为二阶。它被证明是一致和保守的，其解决方案被证明可以保留伽利略不变性和能量定律。数值测试表明，所提出的模型和方案对于研究各种具有挑战性的多相和多组分流动是有效且稳健的。针对所提出的模型开发了相应的数值方案，其形式精度在时间和空间上均为二阶。它被证明是一致和保守的，其解决方案被证明可以保留伽利略不变性和能量定律。数值测试表明，所提出的模型和方案对于研究各种具有挑战性的多相和多组分流动是有效且稳健的。