流体力学新型通用函数Y的变分有限元分析

本文应用通用函数Y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。将物理平面变换成映象平面。在映象平面上,引出通用函数Y,并且写出关于Y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,该方法是非常有效的。

A Variational Finite Element Analysis with A New General Function Y of Fluid Mechanics

In this paper, a general function Y and its variational principles are applied 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 Y is introduced and the variational principle concerning the function Y is written. The solution of the gravity-influenced free surface flows by means of variational principles and finite element method overcome the difficulty of the unknown free surface boundary. Thus, a new way for solving gravity-influenced free surface flows is found. The solution of the dam out flow problem is cited as an example. The result shows that this method is very effective.