Knowledge Management System of Institue of Mechanics, CAS
| 若干流体力学问题的数学性质研究 | |
李明军
| |
| Thesis Advisor | 高智 |
| 2002 | |
| Degree Grantor | 中国科学院力学研究所 |
| Place of Conferral | 北京 |
| Subtype | 博士后 |
| Degree Discipline | 流体力学 |
| Keyword | 湍流大小尺度（lss）方程组 相似的相互作用结构 抛物化稳定性方程组 变步长摄动有限差分格式 Large-small Scale (Lss) Equations Of Turbulence The Similar Structure The Parabolized Stability Equations (Pse) Non-uniform Scale Perturbation Finite Difference Scheme |
| Other Abstract | 该文利用高智的扩散抛物化方程组理论及流体力学基本方程组的特征次特征理论,流体大小尺度（LSS）方程组理论以及摄动有限差分（PFD）方法,研究若干流体力学问题的数学性质.该文得到的主要结论有：1.利用湍流大小尺度（LSS）方程组推导出湍流大小尺度涡量（LSSV）方程组,并证明两个关于湍流大小尺度涡量的命题,从而得到湍流封闭大小尺度涡量（CLSSV）方程组,并对已有的近程相互作用命题进行推广.2.根据扩散抛物化方程组理论和流体力学层次结构方程组的特征和次特征方法,研究了抛物化稳定性方程组（PSE）的特征和次特征以及消除PSE的剩余椭圆特性的问题.3.利用摄动有限差分（PFD）方法得到对流扩散反应方程的变步长摄动有限差分格式,是等步长摄动有限差分格式的推广.; In this thesis, by using the theory of the parabolized equations and its Characteristic analysis on the basic equations of the fluid mechanics, the theory of the large-small scale (LSS) equations of turbulence, and the method of the perturbation finite difference (PFD), which are firstly investigated by Gao Zhi, mathematical properties on some questions of fluid mechanics are investigated. Our main results are the following: By using the theory of large-small scale equations of turbulence, the large-small scale vortex equations of turbulence are gained. Then, two propositions are listed, and the closed large-small scale vortex equations of turbulence are obtained. Then, the proposition of contiguous interactions is generalized. On the same time, Under the basis of the viscous-inviscid interacting flow theory and the grade stracture theory for the basic equations of fluid mechanics(BEFM), the physics scales of two dimension turbulence are analyzed, and the similar structure of the averaging component of the velocity and the fluctuating component of the velocity of two dimension turbulence are educed. By using characteristic and sub-characteristic theories, we can remove the remained ellipticity from the parabolized stability equations (PSE), and our results for the linear PSE are consistent with a known result, and we also give the influence of the Mach number out. At the same time, we further obtain the methods of removing the remained ellipticity from the nonlinear PSE. The physics scales and their relations of the fluid mechanics equations are investigated on the strong viscous shear flow. Gridding critical scale (GCS) analysis is also done on the strong viscous fluid stability equations. Then, some questions are resolved on the strong viscous fluid stability equations. As applications, a new simplified form of Orr-Sommerfeld equation is gained. By using the perturbation finite difference (PFD) method, non-uniform scale perturbation finite difference scheme on the convective-diffusion equations gained, which is a generalization of PFD scheme. The properties and typical numerical results show that non-uniform scale perturbation finite difference scheme is high-order-accurate and high-resolution difference scheme that compare with lst-order-accurate upwind difference schemes and 2nd-order-accurate center difference schemes. On the same time, by using the PFD method and the Von Neumann law which is a rule used to determinant stability of the difference equations of initial-value problems, the perturbation finite difference method of the hyperbolic equations and its stability condition are obtained. |
| Call Number | 30002 |
| Language | 中文 |
| Document Type | 学位论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/23324 |
| Collection | 力学所知识产出(1956-2008) |
| Recommended Citation GB/T 7714 | 李明军. 若干流体力学问题的数学性质研究[D]. 北京. 中国科学院力学研究所,2002. |
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| 若干流体力学问题的数学性质研究.pdf（8373KB） | 开放获取 | -- | Application Full Text | |||
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