| 关于Orr—Sommerfeld方程的Chebyshev谱方法的讨论 |
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| 引用本文： | 孙德军,尹协远.关于Orr—Sommerfeld方程的Chebyshev谱方法的讨论[J].上海力学,1998,19(1):1-8. |
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| 作者姓名： | 孙德军 尹协远 |
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| 作者单位： | 中国科技大学力学和机械工程系，中国科技大学力学和机械工程系，中国科技大学力学和机械工程系 合肥 230026，合肥 230026，合肥 230026 |
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| 摘 要： | 本文讨论了Ｏｒｒ－Ｓｏｍｍｅｒｅｌｄ方程的各种Ｃｈｅｂｙｓｈｅｖ谱离散方法，数值证明了Ｃｈｅｂｙｓｈｅｖ配置法离散Ｏｒｒ－Ｓｏｍｍｅｒｆｅｌｄ方程没有伪谱，并以此构造了适于任意平面平行速度剖面情形，对时间和时空稳定性模式一致有效的无伪谱的离离散方法，其中，对时空稳定性问题本文给出了一种新的迭代法可以快速有效地求出复频率的鞍点，对平面Ｐｏｉｓｅｕｉｌｌｅ流，Ｂｌａｓｉｕｓ边界层流和Ｇａｕｓｓ模型尾迹
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| 关 键 词： | 稳定性 谱方法 O－S方程 平面流 边界层 尾迹 |
ON CHEBYSHEV SPECTRAL METHODS FOR THE ORR-SOMMERFELD EQUATION |
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| Sun Dejun Yin Xieyuan Tong Binggang.ON CHEBYSHEV SPECTRAL METHODS FOR THE ORR-SOMMERFELD EQUATION[J].Chinese Quarterly Mechanics,1998,19(1):1-8. |
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| Authors: | Sun Dejun Yin Xieyuan Tong Binggang |
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| Abstract: | In this paper, a discussion about various Chebyshev spectral methods for the Orr-Sommer-feld equation is given. Firstly it is proved numerically that no spurious mode may be yield by the Chebyshev collocation method; then an uniformly available Chebyshev colocation method free from the spurious mode is developed for temporal and temporal-spatial stability problem of an arbitrary plane velocity profile. For the temporal-spatial stability problem, a new iterative method for solving the saddle point of the complex frequency is then proposed. Examples for the plane Poiseuille flow, the Blasius veloctiy profile and the Gaussian model wake profile give very good results. |
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| Keywords: | stability Orr-Sommerfeld equation spectral method |
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