二维流面上的流动问题的速度图方法  

Hodograph Method of Flow on Two-Dimensional Manifold

作　　者：李开泰[1] 史峰[1] 

机构地区：[1]西安交通大学理学院,西安710049

出　　处：《应用数学和力学》2010年第3期337-350,共14页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10971165;10771167;10926080)

摘　　要：对于一些特殊的流动,尤其是平面上的位势流动,速度图方法有其显著的优点.对于理想流体来说,流面总是存在的,在流面上,流动的速度向量总是在其切空间里.通过引入流函数和势函数,采用张量分析作为工具,给出了二维曲流面上位势流动的速度图方法,得到了流函数满足的速度图方程,为一些特殊的流动问题提供了一类分析方法.并且,对于得到的二维速度图方程,得到了相应的特征方程和特征根,从而可以对方程的类型进行分类.最后,给出了一些特殊流动的实例.For some special flow, especially the potential flow in the plane, there are obvious advantages using the tool of hodograph method. For the realistic flow, there exists stream surface, namely, two-dimensional manifold, on which the velocity vector of the flow lies its tangent space. By introducing the stream function and potential function, the hodograph method for potential flow on a surface was established with the help of tensor analysis, which provided a kind of analysis method. For the derived hodograph equation, the characteristic equation and its characteristic roots were also derived, from which the type of the hodograph equation of the second order can be classified. Moreover, some examples for special surfaces were given.

关 键 词：速度图方法 位势流 流面 流函数 位势函数 

分 类 号：O175.1[理学—数学]