| 二维Woods-Burnett方程的稳定性分析 |
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| 引用本文： | 魏淑惠,包福兵,朱赠好.二维Woods-Burnett方程的稳定性分析[J].空气动力学学报,2012,30(1):90-94. |
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| 作者姓名： | 魏淑惠 包福兵 朱赠好 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金，浙江省自然科学基金 |
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| 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.
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| 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 |
Linearized stability analysis of two-dimensional Woods-Burnett equations |
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| WEI Shu-hui
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BAO Fu-bing
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ZHU Zeng-hao.Linearized stability analysis of two-dimensional Woods-Burnett equations[J].Acta Aerodynamica Sinica,2012,30(1):90-94. |
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| Authors: | WEI Shu-hui BAO Fu-bing ZHU Zeng-hao |
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| Institution: | 1 College of Mathematics Science and Technology,Northeast Petroleum University,Daqing 163318,China; 2 Institute of Fluid Measurement and Simulation,China Jiliang University,Hangzhou 310018,China) |
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| Abstract: | 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. |
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| Keywords: | Woods-Burnett equations linearized stability analysis critical Knudsen number rarefied gas flow |
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