三峡库区枝状河网水动力过程实时模拟
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摘要
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<10cm,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。
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 prediction-correction method to decompose the sparse linear system of dendritic river network to several tridiagonal systems. 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 errors 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.
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 prediction-correction method to decompose the sparse linear system of dendritic river network to several tridiagonal systems. 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 errors 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.
引文
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[4]夏军强,张晓雷,邓珊珊,等.黄河下游高含沙洪水过程一维水沙耦合数学模型[J].水科学进展,2015,26(5):686-697.
[5]陈炼钢,施勇,钱新,等.闸控河网水文-水动力-水质耦合数学模型——Ⅰ.理论[J].水科学进展,2014,25(4):534-541.
[6]HU De-chao,ZHONG De-yu,WANG Guang-qian,et al.A Semi-implicit Three-dimensional Numerical Model for Non-hydrostatic Pressure Free-surface Flows on an Unstructured,Sigma Grid[J].International Journal of Sediment Research,2013,28(1):77-89.
[7]HU De-chao,ZHANG Hong-wu,ZHONG De-yu.Properties of the Eulerian-Lagrangian Method Using Linear Interpolators in a Three-dimensional Shallow Water Model Using z-level Coordinates[J].International Journal of Computational Fluid Dynamics,2009,23(3):271-284.
[8]HU De-chao,ZHONG De-yu,ZHANG Hong-wu,et al.Prediction-Correction Method for Parallelizing Implicit 2D Hydrodynamic Models.I:Scheme[J].Journal of Hydraulic Engineering,2015,141(8):04015014.
[9]黄仁勇.长江上游梯级水库泥沙输移与泥沙调度研究[M].北京:科学出版社,2017:14-16.