第三类边界条件的扩散波洪水演算研究

Flood propagation using the diffusion wave equation with the third type of boundary condition downstream

扩散波方法被理论和实际洪水演算证明是一种既具有足够精度又相对简单的方法 ,并且广泛地应用于河道洪水演算之中。长期以来针对河道的上下边界条件均为流量或水位过程线的研究进行得较为深入 ,而对边界条件为水位流量关系的研究较为少见。基于河道下边界的水位流量关系和圣维南方程组中动力方程的联立求解 ,利用小扰动分析方法 ,导出了第三类下边界条件。利用 L aplace变换法以及数值求解 L aplace逆变换的 Crum p方法 ,得到了扩散波方程在该边界条件下的解析解。研究示例表明 。

The diffusion equation is shown to be accurate enough, to calculate flood propagation. Many projects have used the diffusion equation with the upstream and downstream boundary conditions as hydrographs or discharge only, but not with water height versus discharge as the boundary condition. The stage discharge curve at the downstream boundary is combined with the momentum equation of the St. Venant equations to create a third type boundary condition for the downstream condition. The Laplace transform method is used to solve the diffusion equation with the boundary condition. A case study indicates that the proposed method can adequatly calculate channel flood propagation.