用碰撞频率与速度有关的动力学模型捕捉稀薄气体流动中分子间势的影响
Capturing the influence of intermolecular potential in rarefied gas flows by a kinetic model with velocity-dependent collision frequency
摘要：
本文提出了一种称为$ν$ -模型的动力学模型来代替复杂的Boltzmann碰撞算符，用于模拟稀薄单原子气体的流动。该模型遵循弛豫时间近似，但碰撞频率（即弛豫时间的倒数）是分子速度的函数，反映了Boltzmann方程中的部分碰撞细节，且弛豫所对应的目标速度分布函数（VDF）与Shakhov模型中的VDF接近.在数值模拟强非平衡激波的基础上，针对不同的分子间相互作用势，设计了一种半理论半经验的碰撞频率，大大提高了$ν$模型的计算精度，并分析了其产生机理. $ν$ -模型也表现出良好的典型稀薄微流，特别是在热蒸腾，其中与速度无关的碰撞频率的传统动力学模型缺乏区分的能力，分子间的潜力的影响。
英文摘要：
A kinetic model called the $ν$-model is proposed to replace the complicated Boltzmann collision operator in the simulation of rarefied flows of monatomic gas. The model follows the relaxation-time approximation, but the collision frequency (i.e, inverse relaxation time) is a function of the molecular velocity to reflect part of the collision details of the Boltzmann equation, and the target velocity distribution function (VDF) to which the VDF relaxes is close to that used in the Shakhov model. Based on the numerical simulation of strong non-equilibrium shock waves, a half-theoretical and half-empirical collision frequency is designed for different intermolecular potentials: the $ν$-model shows significantly improved accuracy, and the underlying mechanism is analysed. The $ν$-model also performs well in canonical rarefied micro-flows, especially in the thermal transpiration, where the conventional kinetic models with velocity-independent collision frequency lack the capability to distinguish the influence of intermolecular potentials.
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