论文标题
反应性四级气态混合物的玻尔兹曼方程的力矩方法
Moment Method for the Boltzmann Equation of Reactive Quaternary Gaseous Mixture
论文作者
论文摘要
我们有兴趣使用Grad'S-14力矩方法来解决化学反应稀疏气体流动的玻尔兹曼方程。我们首先提出了一个新型的数学模型，该模型描述了化学反应硬球的碰撞动力学。使用碰撞模型，我们提出了一种算法来计算Boltzmann碰撞运算符的矩。我们的算法是一般的，因为它可以用于计算碰撞操作员的任意顺序矩，而不仅仅是Grad'S-14时刻系统中包含的矩。对于一阶化学动力学，我们得出了平衡以外的化学反应的反应速率，从而扩展了仅在平衡中有效的Arrhenius定律。我们表明，衍生的反应速率（i）是一致的，因为在平衡时，我们恢复了Arrhenius定律，并且（ii）明确依赖于标量第十四刻，强调了考虑14个力矩系统而不是13个。通过数值实验，我们研究了毕业生14矩系统对平衡状态的松弛。
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.
