基于有限差分法的跌坎冲刷一维数值模拟  

One-dimensional numerical simulation of riverbed headcut erosion process based on finite difference method

作　　者：张雪[1] 王新宏[1] 董梁 郎永彪 倪宇航 ZHANG Xue;WANG Xinhong;DONG Liang;LANG Yongbiao;NI Yuhang(State Key Laboratory of Eco-hydraulics in Northwest Arid Region,Xi’an University of Technology,Xi’an 710048,China;Qinghai Water Resources&Hydro Power Reconnaissance Design Research Institute,Xining 810001,China)

机构地区：[1]西安理工大学省部共建西北旱区生态水利国家重点实验室,陕西西安710048 [2]青海省水利水电勘测设计研究院,青海西宁810001

出　　处：《水资源与水工程学报》2021年第1期172-178,186,共8页Journal of Water Resources and Water Engineering

基　　金：陕西省水利科技项目(2017slkj-18、2018slkj-3)。

摘　　要：跌坎冲刷是一种特殊的河床冲淤现象,涉及跨临界流以及剧烈的河床变形过程,数值模拟时由于Preissmann格式仅适用于模拟无间断点的连续水流,无法模拟跨临界流即有间断点存在的情形,因此常出现因急、缓流交替引起的数值振荡问题。基于此,依据河道各断面弗劳德数Fr的大小识别间断点所在位置,将河道划分为不同流段,确保各流段为相同流态的连续水流,对缓流、急流、水跃、水跌4种情况提出合适的边界条件分别进行离散求解,建立基Preissmann格式的跨临界流跌坎冲刷一维非恒定推移质输移数学模型。并利用水槽试验资料对数学模型进行验证,结果表明模型预测值与实测值吻合较好,说明所建立的跌坎冲刷模型预测的可靠性和适用性。Headcut erosion is a special phenomenon of riverbed erosion and deposition,involving transcritical flows and severe riverbed deformation processes.In the numerical simulation of the erosion process,the numerical oscillation caused by the alternating of torrent and slow flow often occurs.The main reason for this problem is that the Preissmann scheme is only suitable for simulating continuous water flows without interruption points,it cannot simulate transcritical flow because of the occurrence of interruption points.According to the Froude number of each cross-section,the position of each interruption point was identified,and the channel was divided into different flow sections to ensure that each flow section had a continuous flow with the same flow pattern.Appropriate boundary conditions were proposed for the four cases of slow flow,rapid flow,hydraulic jump and water fall,respectively.Then a one-dimensional mathematical model of unsteady riverbed mass transport based on Preissmann scheme for transcritical flow headcut erosion was established,which was verified afterwards using flume test data.The results show that the predicted value is in good agreement with the measured value,demonstrating the reliability and applicability of the model.

关 键 词：跌坎冲刷 跨临界流 非恒定流 有限差分法 PREISSMANN格式 

分 类 号：TV131.4[水利工程—水力学及河流动力学]