A modified form of BGK source terms is proposed for modeling two-phase flows with thermodynamical disequilibrium. The novelty is that three independent time-scales allow to manage the return to the thermodynamical equilibrium while remaining in agreement with the second law of thermodynamics. This is achieved thanks to the definition of a “local-in-time” equilibrium state which tends toward the asymptotic equilibrium state when time increases. The thermodynamical paths of the system are then modified with respect to the classical BGK source terms used for two-phase flow modeling, and the relaxation process of the system toward the asymptotic equilibrium state can be defined with additional degrees of freedom. In a numerical point of view, both the classical and the modified BGK source terms have advantages. The choice between these two forms strongly depends on the numerical strategy used to perform simulations.

提出了一种修改形式的 BGK 源项，用于模拟具有热力学不平衡的两相流。新颖之处在于三个独立的时间尺度允许管理返回到热力学平衡，同时保持与热力学第二定律一致。这要归功于“时间局部”平衡状态的定义，当时间增加时，该平衡状态趋于渐近平衡状态。然后根据用于两相流建模的经典 BGK 源项修改系统的热力学路径，并且可以用额外的自由度定义系统向渐近平衡状态的弛豫过程。从数值的角度来看，经典和修改后的 BGK 源项都有优势。