考虑分子转动自由度的离散统一气体动理学格式

Discrete unified gas kinetic scheme for diatomic gas with rotational degrees of freedom

离散统一气体动理学格式(DUGKS)是一种适用于全流域模拟的有限体积方法。之前的研究考虑了分子平动自由度,验证了DUGKS在多尺度问题中的准确性及稳定性。本文基于Rykov模型方程构造了离散统一气体动理学格式,并采用Landau-Teller-Jeans转动能量松弛模型,可用于双原子气体从连续流动到稀薄流动的多尺度问题计算。测试了激波结构、超声速平板绕流以及超声速圆柱绕流等非平衡流动问题,计算结果显示出双原子气体分子中存在平动自由度与转动自由度对应的能量交换过程,并与统一气体动理学格式(UGKS)、直接蒙特卡罗(DSMC)方法的解以及实验值吻合较好。

The Discrete Unified Gas Kinetic Scheme(DUGKS)is a finite volume method suitable for all Knudsen number regimes.Previous studies considering molecular translational degrees of freedom have verified the accuracy and stability of DUGKS in multiscale problems.In this paper,the DUGKS is constructed based on the Rykov gas kinetic equation,and the Landau-Teller-Jeans rotational energy relaxation model is used.Then the DUGKS can be used in multiscale problem calculation from continuum flow to rarefied flow for diatomic gases.Some non-equilibrium cases,such as one-dimensional shock structure,the hypersonic flow passing a flat plate,and the hypersonic flow around a cylinder have been tested.The results show the existence of energy exchange process corresponding to the degrees of freedom of translation and rotation in diatomic gas molecules.And the calculation results are in good agreement with the Unified Gas Kinetic Scheme(UGKS),Direct Simulation Monte Carlo(DSMC),and experimental values.