【摘要】 用有限元法计算水力学问题的困难之一是如何处理自由水面.因自由水面的位置在计算前是不知道的,求解的区域就不能预先确定.常用的方法是先假定自由水面的位置,把问题当作具有已知边界的问题来计算,然后校核沿自由水面的条件是否满足.如不满足,再重新修改自由水面的位置进行计算,直到能满足为止.本文建议,从可变区域的变分概念出发,把决定自由水面形状的座标和各结点的流函数值当作未知量,形成方程组同时求解.用这种方式可以减少计算的工作量,算出的溢流面压力分布资料和试验结果符合较好.更多还原

【Abstract】 Among the difficult problems in hydraulics is the flow with a free urface,because, not known a priori,it has to be determined as a part of the solution.A finite element method based on the variational principle for variable domains is proposed for this type of problems. As shown in Fig.1, the domain of solution is divided by a prescribed F curve into two sub-domains,the fixed ABEPQGMNOA and the variable EFQPE with the free stream line as its boundary. Triangular elements and linear distribution of ψ are adopted for the inner region,while trapezoidal elements and linear distribution of q2 for the variable domain. The unknowns to be solved for are the values of ψ of the nodes and the ordinates of points on the free surface. Equating the partial derivatives of the functional to zero furnishes enough equations,thus,the location of the free surface and the values of ψ are solved for simultaneously. The method is applied to free surface sluice gate flow over spillway and computed pressure distribution agrees satisfactorily with experimental results.更多还原