流体力学新型通用函数Ω的变分有限元分析

A Variational Finite Element Analysis With a New General Function Ω of Fluid Mechanics

本文应用通用函数Ω及其变分原理,为求解具有自由面流动问题提出了一种新方法。将物理平面变换到映象平面。在映象平面上,引出通用函数Ω,并且写出关于Ω的变分原理。用这个变分原理及有限元法求解自由面流动可克服边界未知的困难。文中以水坝闸门出流问题为例进行了计算,结果表明,该方法是有效的。

In this paper,a general function Ω and its variational principles are employed to solve the problem of gravity-influenced free surface plane flows. First of all, the physical plane is transformed into a new image plane.On the new image plane,the general function Ω is introduced and the variational principle concerning the function Ω is written. The solution of the gravity-influenced free surface flows by means of variational principles and finite element method can be used to overcome the difficulty of the unknown free surface boundary.Thus,a new way to solve the gravity-influenced free surface flows is found.The solution of the dam-out-flow problem is cited as an example. This method has proved to be very effective by the result.