| 二维抛物化稳定性方程的特征分析 |
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| 引用本文： | 涂国华,袁湘江,查俊,陶建军. 二维抛物化稳定性方程的特征分析[J]. 航空学报, 2009, 30(3): 385-390 |
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| 作者姓名： | 涂国华 袁湘江 查俊 陶建军 |
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| 作者单位： | 中国空气动力研究与发展中心,四川绵阳,621000;天津市现代工程力学重点实验室,天津,300072;北京航空航天大学国家计算流体力学实验室,北京,100191;中国空气动力研究与发展中心,四川绵阳,621000;北京航空航天大学国家计算流体力学实验室,北京,100191;北京大学力学与空间工程系和湍流与复杂系统国家重点实验室,北京,100871 |
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| 基金项目： | 国家自然科学基金(1321002,10672012) |
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| 摘 要： | 在对抛物化稳定性方程(PSE)的基本流场没有做任何近似假定的情况下，分析了PSE的特征性质。分析表明，当法向速度不为零时，PSE有一个非零主特征值，其余主特征值都为零。PSE的次特征值与扰动波的空间波数α有关，α的实部代表扰动波的波动情况，它可以直接导致复特征值出现；α的虚部表示扰动波的增长(衰减)情况，当它的绝对值超过一定范围时，也会在边界层内亚声速区的局部区域导致复特征值出现。增大求解PSE的空间推进步长，可以克服PSE的椭圆性。
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| 关 键 词： | 抛物化稳定性方程 特征值 次特征值 可压流 边界层 |
| 收稿时间： | 2007-09-21 |
| 修稿时间： | 2008-12-19 |
Characteristics Analysis of Two-dimensional Parabolized Stability Equations |
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| Tu Guohua,Yuan Xiangjiang,Zha Jun,Tao Jianjun. Characteristics Analysis of Two-dimensional Parabolized Stability Equations[J]. Acta Aeronautica et Astronautica Sinica, 2009, 30(3): 385-390 |
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| Authors: | Tu Guohua Yuan Xiangjiang Zha Jun Tao Jianjun |
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| Affiliation: | 1.China Aerodynamics Research and Development Center 2.Tianjin Key Laboratory of Modern Engineering Mechanics 3.National Laboratory for CFD, Beijing University of Aeronautics and Astronautics 4.LTCS and Department of Mechanics and Aerospace Engineering, Peking University |
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| Abstract: | The characteristics of parabolized stability equations (PSE) are analyzed without any approximate hypothesis of base flows. The analysis indictes that there is a nonzero main characteristic due to the nonzero transverse velocity, and all the other main characteristics of PSE are zero. The sub-characteristics are related to the spacial wave number (α) of a disturbance. The real part of α denotes the wavelength of the disturbance, and a nonzero real part of α leads to complex sub-characteristics. The image part of α denotes the increase/decrease rate of the disturbance, and a nonzero image part of α would lead to complex sub-characteristics if the absolute value of the image part is large enough. The ellipticity of PSE tends to be alleviated by a large matching step size. |
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| Keywords: | parabolized stability equation characteristic sub-characteristic compressible flow boundary layer |
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