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.

我们对使用Grad's-14矩法求解稀有气体流进行化学反应的Boltzmann方程感兴趣。我们首先提出一个新颖的数学模型，该模型描述化学反应硬球的碰撞动力学。使用碰撞模型，我们提出一种算法来计算Boltzmann碰撞算子的矩。我们的算法是通用的，它可以用于计算碰撞算子的任意阶矩，而不仅仅是Grad's-14矩系统中包含的矩。对于一阶化学动力学，我们导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时有效的阿伦尼乌斯定律。我们表明，在平衡的意义上，得出的反应速率（i）是一致的，我们恢复了阿伦尼乌斯定律，并且（ii）明确依赖于标量第十四矩，这突出了考虑使用第十四矩系统而不是第十三矩系统的重要性。通过数值实验，我们研究了Grads-14矩系统到平衡态的弛豫。