稀薄气体动力学矩方法研究综述

临近空间位于航天器入轨与返回的必经区域, 也是临近空间高超声速飞行器长航时飞行空域, 空间环境的特殊性决定了飞行器在穿越时必须考虑稀薄大气环境对飞行器气动力防隔热通讯及控制的影响.Boltzmann方程作为描述气体分子速度分布函数演化规律的微分-积分形式, 在一定条件下能够描述从自由分子流到连续流全流域流动现象.作为Boltzmann方程的宏观表达形式, 矩方程这一经典流体力学方程形式涵盖了Euler方程N-S方程Burnett方程super-Burnett方程及近年来发展的广义流体力学方程——非线性本构关系模型等.由于成熟的CFD数值计算理论及有限矩方程较高的计算效率, 滑移过渡流矩方法相比粒子仿真与Boltzmann模型方程方法具有十分显著的优势和巨大的工程应用潜力.因此, 对近年来传统及新型矩方法研究所取得的进展进行归纳总结, 并针对关键科学问题开展理论与数值计算方法研究, 具有十分重要的理论与工程应用价值. 

A review of moment equations for rarefied gas dynamics

Near space is a special zone where the spacecraft must pass through during reentry and the hypersonic craft cruise. The rarefied environment will undoubtedly have an influence on the aerodynamic characteristics, thermal protection and communication of the craft. As an integral-differential equation, Boltzmann equations can describe the velocity distribution function of the gas from continuum flow to free molecule flow under certain conditions. Moment equations, which are the macroscopic form of Boltzmann equations, include Euler equations, N-S equations, Burnett equations, super-Burnett equations and recently developed generalized hydrodynamic equations. Due to the well-developed numerical methods in computational fluid dynamics and high computational efficiency, moment method has a prominent advantage comparing with particle method and modeled Boltzmann equations. Therefore, the review of the development of moment equations in recent years and the research on the well-known problems are very important both in theory and practice.