非等温多组分扩散界面两相流的熵稳定建模与真实状态方程
Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state
AI总结：
本文提出一种非等温可压缩多组分扩散界面两相流模型，通过热力学定律和Onsager原理推导出一般模型，建立熵稳定数值方法，验证了热力学定律的满足。
摘要：
本文考虑了非等温可压缩多组分扩散界面两相流的数学建模和数值模拟。通过热力学定律和Onsager的互易原理，推导出一个具有通用参考速度的一般模型，能够表征多种流体的压缩性和部分混溶性。证明了压力、温度和化学势之间的新关系，导致动量守恒方程的新形式，表明化学势和温度的梯度成为流体运动的主要驱动力，除了外力之外。数值模拟的关键挑战是开发熵稳定的数值方案，以保持热力学定律。基于Helmholtz自由能密度关于摩尔密度和温度的凸凹分割，提出了一种熵稳定数值方法，直接求解总能量平衡方程，从而自然满足热力学第一定律。通过估计Helmholtz自由能和动能随时间的变化，证明了所提出方法的无条件熵稳定性（热力学第二定律）。数值结果验证了所提出的方法。
英文摘要：
In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is derived rigorously through thermodynamical laws and Onsager's reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation among the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex-concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.
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