反应性四元气体混合物Boltzmann方程的矩量法
Moment Method for the Boltzmann Equation of Reactive Quaternary Gaseous Mixture
摘要：
我们感兴趣的是用格拉德14矩方法求解化学反应稀薄气体流动的玻尔兹曼方程。我们首先提出了一个新的数学模型，描述了化学反应硬球的碰撞动力学。利用碰撞模型，我们提出了一种计算玻尔兹曼碰撞算符矩的算法。我们的算法是通用的，在这个意义上，它可以用来计算任意阶矩的碰撞算子，而不仅仅是包括在格拉德的14时刻系统的时刻。对于一阶化学动力学，我们推导出平衡外化学反应的反应速率，从而扩展了仅在平衡时有效的阿克里先乌斯定律。我们表明，推导出的反应速率（i）是一致的，在这个意义上说，在平衡时，我们恢复的阿克里尼乌斯定律和（ii）有一个明确的依赖于标量的十四阶矩，突出考虑一个十四阶矩系统，而不是一个十三阶矩的重要性。通过数值实验，研究了Grad-14矩系统向平衡态的弛豫过程.
英文摘要：
We are interested in solving the Boltzmann equation of chemically reacting rarefied gas flows using the Grad's-14 moment method. We first propose a novel mathematical model that describes the collision dynamics of chemically reacting hard spheres. Using the collision model, we present an algorithm to compute the moments of the Boltzmann collision operator. Our algorithm is general in the sense that it can be used to compute arbitrary order moments of the collision operator and not just the moments included in the Grad's-14 moment system. For a first-order chemical kinetics, we derive reaction rates for a chemical reaction outside of equilibrium thereby, extending the Arrhenius law that is valid only in equilibrium. We show that the derived reaction rates (i) are consistent in the sense that at equilibrium, we recover the Arrhenius law and (ii) have an explicit dependence on the scalar fourteenth moment, highlighting the importance of considering a fourteen moment system rather than a thirteen one. Through numerical experiments we study the relaxation of the Grad's-14 moment system to the equilibrium state.
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