Title: Compressible N-phase fluid mixture models Show Chinese title

Title: 可压缩多相流混合模型

Abstract: Fluid mixture models are essential for describing a wide range of physical phenomena, including wave dynamics and spinodal decomposition. However, there is a lack of consensus in the modeling of compressible mixtures, with limited connections between different classes of models. On the one hand, existing compressible two-phase flow models accurately describe wave dynamics, but do not incorporate phase separation mechanisms. On the other hand, phase-field technology in fluid dynamics consists of models incorporating spinodal decomposition, however, a general phase-field theory for compressible mixtures remains largely undeveloped. In this paper, we take an initial step toward bridging the gap between compressible two-phase flow models and phase-field models by developing a theory for compressible, isothermal N-phase mixtures. Our theory establishes a system of reduced complexity by formulating N mass balance laws alongside a single momentum balance law, thereby naturally extending the Navier-Stokes Korteweg model to N-phases and providing the Navier-Stokes Cahn-Hilliard/Allen-Cahn model for compressible mixtures. Key aspects of the framework include its grounding in continuum mixture theory and its preservation of thermodynamic consistency despite its reduced complexity. Show Chinese abstract

Abstract: 流体混合模型对于描述一系列物理现象至关重要，包括波动力学和旋节分解。 然而，在可压缩混合物的建模方面尚无共识，不同类别的模型之间的联系有限。 一方面，现有的可压缩两相流模型能够准确描述波动力学，但未包含相分离机制。 另一方面，流体力学中的相场技术包含旋节分解的模型，然而，针对可压缩混合物的通用相场理论仍大多未被开发。 在本文中，我们通过为可压缩、等温的N相混合物建立一种理论，初步尝试弥合可压缩两相流模型与相场模型之间的差距。 我们的理论通过制定N个质量平衡定律和一个动量平衡定律，建立了简化复杂度的系统，从而自然地将Navier-Stokes Korteweg模型扩展到N相，并为可压缩混合物提供了Navier-Stokes Cahn-Hilliard/Allen-Cahn模型。 该框架的关键方面包括其基于连续介质混合理论，以及尽管复杂度降低但仍保持热力学一致性。