Abstract Hydrodynamic simulation of fluids in vessels is often based on the internal energy (U), volume (V), and the number of moles of all components (re N = N 1 , N 2 , … , N n ) as the working variables to determine the thermodynamic state by finding the global maximum of entropy. The procedure of finding the equilibrium state may be divided into two steps: stability analysis and phase-split computations. Stability analysis is performed first, and the phase-split computation proceeds if the system is unstable. Most of the past work on UVN space has been based on phase-split computations, while the stability analysis is barely investigated. Furthermore, previous studies for the stability analysis use only Newton's method to solve the non-linear algebraic equations. We present an efficient and robust approach for stability analysis where UVN is specified. The successive substitution iteration (SSI) is used to provide good initial guesses for Newton's method. The proposed approach results in a reduced number of unknowns and does not require a large number of iterations to achieve convergence in Newton's method. Our proposed formulation is compatible with different equations of state and is applicable to both pure component and multi-components. The robustness and efficiency of the algorithm for stability analysis are demonstrated in various examples.

中文翻译：

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内能、体积和摩尔数 (UVN) 空间中高效且稳健的稳定性分析

摘要 容器中流体的流体动力学模拟通常以内能 (U)、体积 (V) 和所有组分的摩尔数 (re N = N 1 , N 2 , … , N n ) 作为工作变量通过找到熵的全局最大值来确定热力学状态。寻找平衡状态的过程可以分为两个步骤：稳定性分析和分相计算。首先进行稳定性分析，如果系统不稳定，则进行分相计算。过去在 UVN 空间上的大部分工作都基于分相计算，而几乎没有研究稳定性分析。此外，以前的稳定性分析研究仅使用牛顿法来求解非线性代数方程。我们提出了一种有效且稳健的稳定性分析方法，其中指定了 UVN。连续替换迭代 (SSI) 用于为牛顿方法提供良好的初始猜测。所提出的方法减少了未知数，并且不需要大量的迭代来实现牛顿方法的收敛。我们提出的公式与不同的状态方程兼容，适用于纯组分和多组分。稳定性分析算法的鲁棒性和效率在各种例子中得到了证明。所提出的方法减少了未知数，并且不需要大量的迭代来实现牛顿方法的收敛。我们提出的公式与不同的状态方程兼容，适用于纯组分和多组分。稳定性分析算法的鲁棒性和效率在各种例子中得到了证明。所提出的方法减少了未知数，并且不需要大量的迭代来实现牛顿方法的收敛。我们提出的公式与不同的状态方程兼容，适用于纯组分和多组分。稳定性分析算法的鲁棒性和效率在各种例子中得到了证明。