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浙江大学学报(工学版)
浙江大学学报(工学版)  2020, Vol. 54 Issue (3): 614-622    DOI: 10.3785/j.issn.1008-973X.2020.03.023
水利工程     
基于孔隙率和局部时间步长的城市洪水模拟
李薇(),邹吉玉,胡鹏*()
浙江大学 海洋学院，浙江 杭州 310058
Urban flood simulation based on porosity and local time step
Wei LI(),Ji-yu ZOU,Peng HU*()
Ocean College, Zhejiang University, Hangzhou 310058, China
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摘要：

为提高城市洪水模拟的计算效率，在有限体积法框架下，基于能自动捕捉激波、间断的高精度Harten-Latex-van Leer-Contact （HLLC）近似黎曼算子，并结合局部时间步长技术，建立满足静水平衡特性的各向异性孔隙率浅水模型. 经典城市洪水模拟结果表明，所建立的模型能够精确模拟洪水传播过程的复杂流动现象，并能显著提升计算效率：孔隙率方法降低了建筑物周围网格加密的要求，能使计算效率提升一个数量级；局部时间步长技术让每个网格采用尽可能大的时间步长，减少了循环次数，可进一步提升计算效率约2.0~3.0倍.
关键词： 各向异性孔隙率;  浅水方程;  城市洪水模拟;  局部时间步长;  有限体积法    
Abstract:

A well-balanced shallow water model of anisotropic porosity was developed under the framework of finite volume method, in order to increase the computational efficiency of urban flood simulation. The high-resolution Harten-Latex-van Leer-Contact (HLLC) approximate Riemann solver which could automatically capture shockwaves and discontinuities was used for flux computation, together with the local time step technique for time updating. The application to classic idealized urban floods shows that the represent model can accurately reproduce the complex hydrodynamics of urban floods and increase the computational efficiency markedly: the anisotropic porosity method reduces the requirement of local grid refining around obstructions and increases the computational efficiency by an order of magnitude; the local time step technique allows each grid to use a relatively large time step and reduces the temporal iteration, and further saves the computation cost by about two to three times.
Key words: anisotropic porosity    shallow-water equation    urban flood simulation    local time step    finite volume method
收稿日期: 2019-04-11 出版日期: 2020-03-05
CLC:  TV 131.2  
基金资助: 国家重点研发计划资助项目（2016YFC0402305-02）；国家自然科学基金资助项目（11872332，11772300）；浙江省自然科学基金资助项目（LR19E090002）；浙江大学-舟山市市校联合资助项目（K18-529112-004）
通讯作者: 胡鹏     E-mail: lw05@zju.edu.cn;pengphu@zju.edu.cn
作者简介: 李薇（1984—），女，副教授，从事河流海岸动力学、水沙模拟研究. orcid.org/0000-0002-6016-052X. E-mail： lw05@zju.edu.cn
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引用本文:

李薇,邹吉玉,胡鹏. 基于孔隙率和局部时间步长的城市洪水模拟[J]. 浙江大学学报(工学版), 2020, 54(3): 614-622.

Wei LI,Ji-yu ZOU,Peng HU. Urban flood simulation based on porosity and local time step. Journal of ZheJiang University (Engineering Science), 2020, 54(3): 614-622.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.03.023    或    http://www.zjujournals.com/eng/CN/Y2020/V54/I3/614

图 1  三角网格下孔隙率的概念模型图
图 2  理想城市洪水实验布置图
图 3  各计算方案在建筑物区域的网格划分图
图 4  测点水深随时间的变化（平衡算例1）
图 5  不同时刻的水位和地形三维视图（平衡算例2）
图 6  方案C_C和P_RN在10 s时的水深等值线对比图
图 7  理想化城市洪水实验不同测点处水深随时间的变化
图 8  理想化城市洪水实验不同时刻沿街道y=2 m的水深
图 9  理想化城市洪水实验在不同时刻沿街道y=2 m的流速
图 10  各方案在不同局部时间步长（LTS）最大更新层级情况下的计算时间加速倍数
方案 ${ { {\delta} }_{ {\rm{h} }g} }$/m ${ { {\delta} }_{ {\rm{hs} } } }$/m ${ { {\delta} }_{\rm{V} } }$/（m·s–1）
测点1 测点18 测点44 测点55 t=4 s t=5 s t=6 s t=10 s t=4 s t=5 s t=6 s t=10 s
C_C 0.042 0.015 0.022 0.032 0.030 0.023 0.022 0.013 0.466 0.253 0.196 0.135
P_CG 0.032 0.019 0.037 0.027 0.034 0.036 0.038 0.024 0.325 0.292 0.317 0.194
P_CN 0.030 0.017 0.028 0.026 0.033 0.041 0.040 0.023 0.297 0.384 0.288 0.263
P_MN 0.038 0.013 0.028 0.023 0.023 0.017 0.021 0.014 0.309 0.212 0.144 0.121
P_RN 0.034 0.013 0.031 0.024 0.023 0.017 0.020 0.014 0.330 0.205 0.174 0.159
表 1  不同方案的计算值与实测值的误差比较
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