Consistent and conservative scheme for incompressible two-phase flows using the conservative Allen-Cahn model
Consistent and conservative scheme for incompressible two-phase flows using the conservative Allen-Cahn model
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DOI：
10.1016/j.jcp.2020.109718
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发表时间：
2020-07
期刊：
影响因子：
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通讯作者：
Ziyang Huang;G. Lin;A. Ardekani
中科院分区：
文献类型：
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作者：
Ziyang Huang;G. Lin;A. Ardekani
在本工作中，我们考虑了保守的Allen-Cahn模型，并以一致和保守的方式将其应用于两相流动。利用一个辅助变量，将守恒的Allen-Cahn方程改写为守恒形式，得到了一致的公式。因此，进行了一致性分析，所得到的两相模型遵守约化的一致性、质量守恒的一致性以及质量和动量输运的一致性，这对于再现物理动量和动能输运、实现质量和动量守恒以及满足两相系统的能量定律是重要的。提出了一种一致的保守方案，并对其性质进行了仔细的分析和验证。为了尊重保守Allen-Cahn模型的最大值原理，我们提出了一种保持格式一致性和守恒性的有界性映射算法。在实际两相流中的应用表明，该格式对复杂的两相流问题具有较好的精度、鲁棒性和有效性。讨论了一致性公式和一致性分析对多相流和改进的Cahn-Hilliard模型的适用性。
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 theconsistency of reduction, theconsistency of mass conservationand theconsistency 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.