In the present work, the Cahn-Hilliard Phase-Field model of incompressible two-phase flows is considered. Conditions needed for consistency of reduction, consistency of mass and momentum transport, and consistency of mass conservation are proposed. The mass flux in the Navier-Stokes equations is defined such that it satisfies the proposed consistency conditions. The analysis in both continuous and discrete levels shows that violation of the consistency conditions result in unphysical solutions and the inconsistent errors are proportional to the density contrast of the fluids. After considering the conservative form of the inertial term, a consistent and conservative scheme for momentum transport is developed. The balanced-force algorithm for the sharp interface model is extended to the surface force derived from the Cahn-Hilliard model. The proposed scheme is formally 2nd-order accurate in both time and space, satisfies the consistency conditions, conserves mass globally and momentum essentially, and is balanced-force, in the discrete level. Its convergence to the sharp interface solution is systematically discussed in cases including large density and viscosity ratios, surface tension, and gravity. Various two-phase flow problems with large density ratios are performed to validate and verify the proposed scheme and excellent agreements with published numerical and/or experimental results are achieved. The proposed scheme is a practical and accurate tool to study two-phase flows, especially for those including large density ratios.

在目前的工作中，考虑了不可压缩两相流的Cahn-Hilliard相场模型。所需条件减少的一致性，质量和动量传输的一致性和质量守恒的一致性被提议。定义Navier-Stokes方程中的质量通量，使其满足建议的一致性条件。连续水平和离散水平的分析均表明，违反稠度条件会导致非物理解，不一致的误差与流体的密度对比成正比。在考虑惯性项的保守形式之后，开发了一致且保守的动量传递方案。尖锐界面模型的平衡力算法扩展到从Cahn-Hilliard模型导出的表面力。所提出的方案在时间和空间上都正式为二阶精度，满足一致性条件，在整体上节省了质量和动量，并且在离散水平上具有平衡力。在包括大的密度和粘度比，表面张力和重力的情况下，系统地讨论了其向尖锐界面解决方案的收敛。进行了各种具有大密度比的两相流动问题，以验证和验证所提出的方案，并与已发表的数值和/或实验结果取得了很好的一致性。所提出的方案是研究两相流的实用且准确的工具，特别是对于那些包含大密度比的流。