二维Woods-Burnett方程的稳定性分析  

Linearized stability analysis of two-dimensional Woods-Burnett equations

作　　者：魏淑惠[1] 包福兵[2] 朱赠好[2] 

机构地区：[1]东北石油大学数学科学与技术学院,黑龙江大庆163318 [2]中国计量学院流体检测与仿真研究所,浙江杭州310018

出　　处：《空气动力学学报》2012年第1期90-94,共5页Acta Aerodynamica Sinica

基　　金：国家自然科学基金(10902104);浙江省自然科学基金(Y6090589)资助

摘　　要：Woods-Burnett方程是Boltzmann方程的二阶近似,是Burnett方程的一种修正,能够描述轻微偏离热力学平衡时的稀薄气体流动。但是Woods-Burnett方程在小扰动下不稳定,这是限制Woods-Burnett方程广泛应用的一个重要原因。本文在一维稳定性分析的基础上,通过线性小扰动理论,首次得到了二维Woods-Burnett方程的稳定性特征方程,并把稳定性方程的解表示在复平面上,得到了二维稳定性特征曲线。通过扰动增长系数和扰动波数的关系,得到二维Woods-Burnett方程的临界努森数为0.130,而一维Woods-Burnett方程的临界努森数为0.184。说明在二维情况下Woods-Burnett方程更加不稳定。The linearized stability analysis of two-dimensional Woods-Burnett equations was studied for the first time.The characteristic stability equation of this equation was first derived and the characteristic curve was achieved.The two-dimensional Woods-Burnett equations are not stable against small perturbations.The critical perturbation wave frequency is 0.642 and the corresponding critical Knudsen number is 0.130.This value is smaller than that of one-dimension equations,which is 0.184.The two-dimensional Woods-Burnett equations are more unstable than one-dimensional Woods-Burnett equations.

关 键 词：Woods-Burnett方程 线性稳定性分析 临界努森数 稀薄气体流动 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]