三峡库区枝状河网水动力过程实时模拟

基于圣维南控制方程组,针对三峡库区朱沱—坝址河段,采用θ半隐方法离散动量方程的水位梯度项,运用欧拉-拉格朗日方法求解动量方程的对流项,利用有限体积法离散连续性方程,结合预测校正法将枝状河网稀疏线性系统分解为若干三对角子系统,建立了一种可实现河网系统速度-压力耦合问题简单、快速及高精度求解的一维枝状河网水流数学模型。选用2005年、2006年实测水位资料对该模型进行率定与验证,水位计算误差一般＜10 cm,流量计算误差一般＜5%,数学模型计算结果与实测资料符合较好,表明模型精度较高。在单核串行效率测试中,模型模拟1 a水流过程耗时约23.7 s,实现了三峡库区枝状河网水动力过程的实时模拟。

Real-time Simulation of Hydrodynamic Process in Dendritic River Network in Three Georges Reservoir Area

A simple 1-D mathematical dendritic river network model of high precision which could rapidly realize the coupling between flow velocity and pressure is built based on Saint-Venant equations. Finite element volume method is employed to discretize equations of continuity, and semi-implicit θ to discretize the water level gradient term of free-surface elevation. Moreover,Eulerian-Lagrangian method is adopted to solve the advection term, and predic-tion-correction method to decompose the sparse linear system of dendritic river network to several tridiagonal sys-tems. The reach from Zhutuo to dam site of Three Gorges Project is taken as a case study. The model is calibrated and validated with measured historical data in 2005 and 2006,and the results demonstrate that the calculation er-rors of water level and discharge are generally within 10% and 5%,respectively. The results of mathematical model are in good accordance with measured data,indicating that the model is of high precision.In the single-core serial efficiency test,the model takes about 23.7 seconds to simulate the flow process of a year,which implies the real-time simulation of hydrodynamic process of dendritic river network in Three Georges reservoir area can be completed.