一种改进的一维河网水动力解法及其应用  

An Improved Hydrodynamic Solution for One-dimensional River Networks and its Applications

作　　者：吴家阳 徐学军[1,2] 程永光 WU Jiayang;XU Xuejun;CHENG Yongguang(Changjiang Institute of Survey,Planning,Design and Research,Wuhan 430010,China;State Key Laboratory of Water Resources Engineering and Management,Wuhan 430072,China)

机构地区：[1]长江设计集团有限公司,湖北武汉430010 [2]武汉大学水资源工程与调度全国重点实验室,湖北武汉430072

出　　处：《工程科学与技术》2025年第2期104-114,共11页Advanced Engineering Sciences

基　　金：国家重点研发计划项目(2022YFC3002703,2021YFC3000102)。

摘　　要：为高效模拟一维河网水动力学过程,解决汊点水位迭代法中每次迭代均需全局求解所致计算效率低的问题,基于明渠非恒定流的格子Boltzmann Bhatnagar-Gross-Krook(BGK)模型,提出了一种改进的一维河网水动力算法。其中,一维圣维南方程组由格子Boltzmann BGK模型数值求解,离散速度矢量采用一维三速(D1Q3)模型描述;河网耦合求解通过汊点水位迭代法实现,各分汊河段在汊点处均采用水位边界条件,每一时步内通过不断迭代修正汊点水位以满足汊点连接条件。因格子Boltzmann BGK模型本质上为显式算法,有效回避了采用隐式算法计算汊点净流量时需多次迭代推求汊点耦合水位的问题。利用环状河网恒定流、环状和树状组合河网非恒定流等典型河网算例验证了所提方法的准确性,通过与原始汊点水位迭代法进行比较,说明本方法能提高河网水动力模拟的计算效率。作为方法在实际算例中应用,以汉江流域2021年秋汛实测水文过程作为输入条件,计算了汉江中下游平原河网的洪水演进过程,对比了汉江中下游各水文站实测、计算和商用软件模拟的洪水过程,通过与特征线法、Preissmann四点隐式差分法等传统一维河网水动力算法对比,说明了本方法可在不损失计算精度和确保汊点连接条件严格成立的前提下,显著提高一维河网水动力求解效率。Objectives A refined approach is introduced to effectively simulate hydrodynamics in one-dimensional(1D)river networks,enhancing the computational efficiency of the traditional junction water stage iteration method.Methods This approach utilizes the lattice Boltzmann Bhatnagar-Gross-Krook(BGK)model,specifically designed for 1D unsteady open-channel flows.The 1D Saint-Venant equations are solved using the lattice Boltzmann BGK model,where discrete velocity vectors are represented by the D1Q3 model.Equilibrium distribution functions are established to recover the 1D Saint-Venant equations through Chapman-Enskog analysis.The method approximates the spatial derivative of the cross-sectional area in the equilibrium distribution functions using a second-order central difference scheme,achieving an overall second-order spatial accuracy.The coupling of the river network is facilitated through the junction water stage iteration method,initially segmenting the network into various sub-reaches.Water level boundary conditions are imposed at the upper and lower boundaries of each sub-reach.At each time step,the coupling water level is iteratively adjusted to maintain connectivity conditions at all junctions.Given that the lattice Boltzmann BGK model inherently employs an explicit algorithm,it eliminates the necessity for multiple iterations to compute the coupling water level.Results Standard verification scenarios,including steady flows in a looped channel network and unsteady flows in combined looped and treelike networks,were simulated to evaluate the accuracy of the refined method.The hydrodynamics of the middle and lower reaches of the Han River during the autumn flood of 2021 were simulated to validate its utility in real-world applications.The results are as follows:1)For the steady flow scenario in a looped channel network,the simulation outcomes were benchmarked against theoretical analyses,achieving a relative error of up to 7.43%.2)In scenarios involving unsteady flows in combined looped and treelike networks,the r

关 键 词：计算水力学 一维河网非恒定流 格子BOLTZMANN方法 汊点水位迭代法 汉江流域 

分 类 号：TV131[水利工程—水力学及河流动力学]