In the present work, we consider the conservative Allen-Cahn model and applied it to two-phase flows in a consistent and conservative manner. The consistent formulation is proposed, where the conservative Allen-Cahn equation is reformulated in a conservative form using an auxiliary variable. As a result, the consistency analysis is performed and the resulting two-phase model honors the consistency of reduction, the consistency of mass conservation and the consistency of mass and momentum transport, which are important to reproduce the physical momentum and kinetic energy transport, to achieve mass and momentum conservation, and to satisfy the energy law of the two-phase system. A consistent and conservative scheme is developed, and its properties are carefully analyzed and validated. In order to honor the maximum principle of the conservative Allen-Cahn model, we proposed a boundedness mapping algorithm, which preserves the properties of consistency and conservation of the scheme. The applications of the consistent formulation and the proposed scheme to realistic two-phase flows show that they are accurate, robust and effective for complicated two-phase problems. The applicability of the consistent formulation and consistency analysis to multiphase flows and to the improved Cahn-Hilliard model is discussed.

在目前的工作中，我们考虑保守的Allen-Cahn模型，并以一致和保守的方式将其应用于两相流。提出了一致的公式，其中使用辅助变量以保守的形式将保守的Allen-Cahn方程重新公式化。结果，进行了一致性分析，得到的两阶段模型尊重还原的一致性，质量守恒的一致性以及质量与动量传递的一致性。对重现物理动量和动能传输，实现质量和动量守恒以及满足两相系统的能量定律非常重要。开发了一个一致且保守的方案，并对其性能进行了仔细的分析和验证。为了尊重保守Allen-Cahn模型的最大原理，我们提出了有界映射算法，该算法保留了该方案的一致性和守恒性。一致的公式和拟议的方案在现实的两相流中的应用表明，它们对于复杂的两相问题是准确，可靠和有效的。讨论了一致的配方和一致性分析在多相流和改进的Cahn-Hilliard模型中的适用性。