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浙江大学学报(工学版)
浙江大学学报(工学版)  2019, Vol. 53 Issue (4): 743-752    DOI: 10.3785/j.issn.1008-973X.2019.04.015
土木工程、海洋工程     
基于局部分级时间步长方法的水沙耦合数学模拟
胡鹏(),韩健健,雷云龙
浙江大学 海洋学院，浙江 舟山 316021
Coupled modeling of sediment-laden flows based on local-time-step approach
Peng HU(),Jian-jian HAN,Yun-long LEI
Ocean College, Zhejiang University, Zhoushan 316021, China
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摘要：

基于局部时间步长（LTS）技术（即在每个计算网格采用局部允许的最大时间步长），建立新的水沙数学模型，提高计算效率. 用非结构三角形网格离散计算区域，采用充分反映水-沙-床相互作用的平面二维完整控制方程组，利用有限体积法求解控制方程，用HLLC近似黎曼算子估算界面数值通量. 对动床溃坝算例的计算表明，当选取合适的局部时间步长级数时，计算效率明显提高（节省计算时间幅度达到68%），精度满足要求. 长江中游太平口水道的工程应用表明，该模型能够在保证精度的前提下，节省高达92%的计算时间.
关键词： 水沙耦合模型;  有限体积法;  计算效率;  局部时间步长    
Abstract:

A new coupled model for sediment-laden flows was established with high computational efficiency by using the local-time-step (LTS) technology (i.e., using locally allowable maximum time step for variable updating at each cell). The governing equations that fully consider the interactions among the water flow, sediment transport and bed topography, were discretized by the finite volume method on unstructured triangular meshes. The inter-cell numerical fluxes were estimated by the HLLC approximate Riemann solver. The numerical case studies of dam-break floods over mobile bed suggested a reduction of the computational cost by 68% when adopting an appropriate LTS level. Engineering application of the model to the Taipingkou waterway of the Changjiang River led to a 92% reduction in the computational cost without losing quantitative accuracy.
Key words: coupled model for sediment-laden flows    finite volume method    computational efficiency    local-time-step
收稿日期: 2018-01-29 出版日期: 2019-03-28
CLC:  TV 142  
作者简介: 胡鹏（1985—），男，副教授，从事水沙动力学和泥沙运动研究. orcid.org/0000-0001-9214-1318. E-mail: pengphu@zju.edu.cn
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引用本文:

胡鹏,韩健健,雷云龙. 基于局部分级时间步长方法的水沙耦合数学模拟[J]. 浙江大学学报(工学版), 2019, 53(4): 743-752.

Peng HU,Jian-jian HAN,Yun-long LEI. Coupled modeling of sediment-laden flows based on local-time-step approach. Journal of ZheJiang University (Engineering Science), 2019, 53(4): 743-752.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2019.04.015    或    http://www.zjujournals.com/eng/CN/Y2019/V53/I4/743

图 1  局部时间步长技术实现流程示意图
图 2  清水定床溃坝算例沿程水深在64 s时的分布图
工况 L Tr L2（h） L2（u）
无摩阻工况 1（GTS） 1.0 0 0
2 0.59 9.5×10?4 0.14
3 0.39 10?2 1.40
4 0.31 4.8×10?2 1.91
5 0.26 1.1×10?1 2.21
6 0.26 9.3×10?2 2.78
有摩阻工况 1（GTS） 1.0 0 0
2 0.57 1.3×10?3 10?2
3 0.36 2.8×10?3 1.8×10?2
4 0.27 5.2×10?3 2.3×10?1
5 0.24 4.3×10?2 7.4×10?1
湿床面工况 1（GTS） 1.0 0 0
2 0.58 2.4×10?3 2.1×10?2
3 0.36 5.7×10?3 5.0×10?2
4 0.36 5.7×10?3 5.0×10?2
表 1  局部时间步长技术模拟定床溃坝水流的成本和精度
图 3  UCL动床溃坝洪水实验水槽的平面布置示意图
图 4  UCL算例6个测点的计算（采用不同L）和实测水位
图 5  UCL算例2个断面冲淤分布的计算（采用不同L）和实测值
L Tr L2（z）/10?4 L2（Δzb）/10?5
1（GTS） 1.0 0 0
2 0.53 1.8 2.8
3 0.32 3.5 7.7
4 0.25 2.3 48
表 2  局部时间步长技术模拟动床溃坝水流的成本和精度
图 6  太平口水道地理位置及网格划分示意图
图 7  太平口水道边界条件
图 8  计算（用不同级数L）所得太平口水道水深分布
图 9  计算（用不同级数L）和实测太平口水道冲淤分布
L Tr L2（h） L2（Δzb） L Tr L2（h） L2（Δzb）
1（GTS） 1.00 0 0 4 0.21 0.18 0.20
2 0.39 0.17 0.19 5 0.12 0.22 0.18
3 0.31 0.17 0.20 6 0.08 0.22 0.19
表 3  局部时间步长技术模拟太平口水道冲淤的成本和精度
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