堤坝溃决水流数学模型及其应用研究
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摘要
我国不少城市都是沿江河而建,有些城市的堤防并未达标,存在着不少险工险段,洪水期间堤防一旦溃决往往给人们的生命和财产造成巨大的损失。因此,研究堤防溃决之后洪水在城区内的演进规律具有重要的现实意义。
本文首先建立了基于无结构网格Godunov格式的适于模拟天然堤坝溃决水流运动的二维有限体积模型。该模型采用混合非结构网格离散计算区域;采用Roe格式的近似Riemann解来计算通过界面处的法向通量;应用TVD-MUSCL格式和Hancock格式将模型的空间和时间精度同时提高到二阶;同时模型中采用了一种简单有效的干湿边界处理技术和时间动步长技术。通过几个经典算例和具有实际地形的堤坝溃决算例验证了该模型具有良好的激波捕捉能力和较高的计算精度,同时较好的满足了和谐性,能够模拟比较复杂的工程实际问题。
城区地形与天然地形最大的不同在于城区一般分布有密集的建筑物,为模拟建筑物对溃决水流产生的影响,本文采用了三种方法:固壁边界法、真实地形法和加大糙率法。通过物理模型的实测数据对三种方法的计算精度以及适用范围进行了比较和分析后,推荐采用真实地形法。
对哈尔滨上游蓄滞洪区的分洪能力以及可能发生的最大洪水进行了计算和分析,得出的结论认为哈尔滨市未来仍有发生溃堤的可能。鉴于此,采用本文二维水流模型对哈尔滨市可能发生的溃堤洪水进行了数值模拟,模型比较合理的模拟了城区溃堤水流的运动,所得的结果合理可靠。为了考虑侵入社区和楼房内的洪水水量,提出了侵入水量的概念,并借用侧堰流的思想给出了这部分水量的估算方法。
为了将数学模型的计算结果更直观有效的显示给防洪决策者,本文采用动态链接库技术将数学模型嵌入三维可视化平台,构建了哈尔滨溃堤洪水三维可视化系统,该系统可以实时显示溃堤洪水在城区内的运动过程,利于防洪决策者方便快捷的制定防洪抢险的最佳方案,提升抗洪抢险的工作效率。
Flood is a major concern for many Chinese cities that are founded along rivers, and there exists a high risk of levee-breach due to low design criteria and poor maintenance. In case of levee-breach, the flood may induce serious losses of lives and properties. Therefore, it is of great significance to study the routing characteristics of flood caused by levee breach.
A two dimensional numerical model based on Godunov method was developed to simulate levee-breach water flows over actual topographies. The Roe’s approximate Riemann solver was used to calculate the flow flux based on the hybrid unstructured finite-volume method. TVD-MUSCL and Hancock methods were used to achieve the second accuracy. A robust procedure was adapted to efficiently and accurately simulate the movement of a wet/dry boundary without diffusing it. The time step was determined adaptively, based on the maximum instantaneous Courant number across the domain. The algorithm’s stability, concordance and robustness were tested with several classical test cases. The test cases with actual topographies showed that the model can be used to deal with complex engineering problems.
Dense buildings in urban areas exert great influence to flash flood, and they were treated in the model as, respectively, (1) solid wall boundaries, (2) grid cells with buildings top elevations, and (3) grid cells with artificially increased roughness. Comparison of the predicating performance of the model with three different approaches showed that approach (2) is more applicable.
Analysis of flood release capacity of upstream detention areas and the probable maximum flood reveals that the risk of levee-breach in Harbin city still exists. The developed 2D model was then applied to describe possible flooding events due to levee breach in Harbin city. The results show that the model can simulate the levee-breach flood well. The invasion coefficient is put forward because the flash flood must invade into the residence block and buildings. In order to compute the invasion water, the side weir idea is used.
In order to display the numerical results visually, the three dimensional levee-breach flood visualization system of Harbin is established by use of the Dll technology to link the numerical model into three dimensional visualization platform. Real-time display of levee-breach flood in the city was realized in the system, and this can help decision makers establish the best scheme about flood control and emergency repair easily and efficiently.
本文首先建立了基于无结构网格Godunov格式的适于模拟天然堤坝溃决水流运动的二维有限体积模型。该模型采用混合非结构网格离散计算区域;采用Roe格式的近似Riemann解来计算通过界面处的法向通量;应用TVD-MUSCL格式和Hancock格式将模型的空间和时间精度同时提高到二阶;同时模型中采用了一种简单有效的干湿边界处理技术和时间动步长技术。通过几个经典算例和具有实际地形的堤坝溃决算例验证了该模型具有良好的激波捕捉能力和较高的计算精度,同时较好的满足了和谐性,能够模拟比较复杂的工程实际问题。
城区地形与天然地形最大的不同在于城区一般分布有密集的建筑物,为模拟建筑物对溃决水流产生的影响,本文采用了三种方法:固壁边界法、真实地形法和加大糙率法。通过物理模型的实测数据对三种方法的计算精度以及适用范围进行了比较和分析后,推荐采用真实地形法。
对哈尔滨上游蓄滞洪区的分洪能力以及可能发生的最大洪水进行了计算和分析,得出的结论认为哈尔滨市未来仍有发生溃堤的可能。鉴于此,采用本文二维水流模型对哈尔滨市可能发生的溃堤洪水进行了数值模拟,模型比较合理的模拟了城区溃堤水流的运动,所得的结果合理可靠。为了考虑侵入社区和楼房内的洪水水量,提出了侵入水量的概念,并借用侧堰流的思想给出了这部分水量的估算方法。
为了将数学模型的计算结果更直观有效的显示给防洪决策者,本文采用动态链接库技术将数学模型嵌入三维可视化平台,构建了哈尔滨溃堤洪水三维可视化系统,该系统可以实时显示溃堤洪水在城区内的运动过程,利于防洪决策者方便快捷的制定防洪抢险的最佳方案,提升抗洪抢险的工作效率。
Flood is a major concern for many Chinese cities that are founded along rivers, and there exists a high risk of levee-breach due to low design criteria and poor maintenance. In case of levee-breach, the flood may induce serious losses of lives and properties. Therefore, it is of great significance to study the routing characteristics of flood caused by levee breach.
A two dimensional numerical model based on Godunov method was developed to simulate levee-breach water flows over actual topographies. The Roe’s approximate Riemann solver was used to calculate the flow flux based on the hybrid unstructured finite-volume method. TVD-MUSCL and Hancock methods were used to achieve the second accuracy. A robust procedure was adapted to efficiently and accurately simulate the movement of a wet/dry boundary without diffusing it. The time step was determined adaptively, based on the maximum instantaneous Courant number across the domain. The algorithm’s stability, concordance and robustness were tested with several classical test cases. The test cases with actual topographies showed that the model can be used to deal with complex engineering problems.
Dense buildings in urban areas exert great influence to flash flood, and they were treated in the model as, respectively, (1) solid wall boundaries, (2) grid cells with buildings top elevations, and (3) grid cells with artificially increased roughness. Comparison of the predicating performance of the model with three different approaches showed that approach (2) is more applicable.
Analysis of flood release capacity of upstream detention areas and the probable maximum flood reveals that the risk of levee-breach in Harbin city still exists. The developed 2D model was then applied to describe possible flooding events due to levee breach in Harbin city. The results show that the model can simulate the levee-breach flood well. The invasion coefficient is put forward because the flash flood must invade into the residence block and buildings. In order to compute the invasion water, the side weir idea is used.
In order to display the numerical results visually, the three dimensional levee-breach flood visualization system of Harbin is established by use of the Dll technology to link the numerical model into three dimensional visualization platform. Real-time display of levee-breach flood in the city was realized in the system, and this can help decision makers establish the best scheme about flood control and emergency repair easily and efficiently.
引文
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