摘要
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。
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.
关键词
流体力学
有限元法
自由面流动
Fluid mechanics
Finite element method
General function
Variational method
Functional equation
Gravity-influenced free surface flows