Boltzmann方程碰撞积分建模与稀薄空气动力学应用研究  

Computable model on the collision integral of Boltzmann equation and application to rarefied aerodynamics

作　　者：吴雷[1] 张勇豪[1] 李志辉[2,3] 

机构地区：[1]思克莱德大学威尔流体实验室 [2]中国空气动力研究与发展中心超高速空气动力研究所,绵阳621000 [3]国家计算流体力学实验室,北京100191

出　　处：《中国科学：物理学、力学、天文学》2017年第7期22-39,共18页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：英国EPSRC基金会(编号:EP/M021475/1;EP/L00030X/1);国家重点基础研究发展计划(编号:2014CB744100);国家自然科学基金(编号:11325212;91530319);英国皇家工程院的杰出访问学者计划(编号:DVF1516/3/57)资助项目

摘　　要：直接模拟蒙特卡罗方法(Direct Simulation Monte Carlo,DSMC)已经广泛用于稀薄空气动力学计算模拟,而直接数值求解Boltzmann方程目前还只局限于简单流动,比如一维线性问题.高度非线性、积分微分属性的Boltzmann方程的求解关键是碰撞积分建模问题.最近,快速谱方法的提出和完善,使得对复杂的三维非线性问题直接求解Boltzmann方程带来了希望.相对于DSMC,快速谱方法具有数值上确定性的优势,在低速多尺度流动计算模拟上更为高效.本文介绍了快速谱方法在求解气体动理学方程的最新发展和成果,并探讨其应用前景.快速谱方法的推广应用使之真正成为DSMC的补充方法,现在面临的困难是需要发展新的气体动理学模型来描述多原子、多组分、稠密气体等.本文最后介绍了这方面的最新进展和直接求解Boltzmann模型方程气体动理论统一算法在模拟计算跨流域气体绕流及航天再入高超声速气动问题的应用.Due to its complexity in dealing with the collisional integral term of the Boltzmann equation and computational costs asso- ciated with multi-dimensional problems, deterministic methods are still restricted to simple flow such as one-dimensional linear flow. However, the recently emerged fast spectrum method has achieved breakthroughs in computational efficiency and accuracy, which can enable simulations for more realistic three-dimensional non-linear flows. In comparison with the dominant direct simulation Monte Carlo method, the deterministic method has advantages especially in simulating low- speed flows where statistical variations prevail. Here, we review the development of fast spectrum method and discuss its applications for practical flow simulations. In particular, extended Boltzmann model is required for polyatomic and dense gases where the Boltzmann equation may not be valid. We present the applications of extended Boltzmann model for polyatomic gases in predicting spectra of both spontaneous and coherent Rayleigh-Brillouin Scattering, and in simulating space vehicle reentries with a broad range of Kn. Finally, we discuss the gas-kinetic unified algorithm （GKUA） of com- putable model Boltzmann equation and applications to the hypersonic aerodynamics of space reentry covering various flow regimes.

关 键 词：稀薄空气动力学 气体动理学模型 离散速度法 BOLTZMANN方程 快速谱方法 气动理论统一算法 

分 类 号：O355[理学—流体力学]