基于二维浅水方程的胖头泡蓄滞洪区洪水演进数值模拟

Numerical Simulation of Flood Evolution in Pangtoupao Flood Storage Area Based on Two-Dimensional Shallow Water Equation

探究蓄滞洪区洪水演进对蓄滞洪区的防洪工作有着重要意义。为在洪水来临时,短时间内对洪水运动进行预测。运用Godunov型有限体积法建立了1个二维浅水水动力数值模型,该模型的的优势在于采用非结构性三角形网格,能够较好地拟合不规则边界,并采用GPU异构并行技术,有效解决了非结构化网计算耗时长的问题,运用限制器减少二阶精度数值的扩散和振荡,引入负水深和干湿边界处理技术,使模型模拟的精确度得到了有效提高。模型应用多个溃坝水流实验算例对模型进行率定,在验证其具有良好的干湿边界计算能力和静水和谐性的基础上,采用嫩江流域1998年洪水数据对嫩江流域的胖头泡蓄滞洪区的洪水演进进行模拟计算。结果显示:模型对胖头泡蓄滞洪区模拟的蓄水量为34.9亿m^(3),与实测值的相对误差为1.7%,洪水淹没面积为1 267.27 km^(2),与实测值的相对误差为9.24%。对研究区域不同的土地类型进行糙率分区的情况下,模型模拟的蓄水量结果更趋近于实测结果。并行化后的程序能使模型计算速度提升33%,因此模型能快速、精准计算复杂地形溃决水流的洪水演进过程。研究结果可以为蓄滞洪区的防洪规划、灾情预警提供相关信息。

Exploring the flood evolution in flood storage areas is of great significance for flood control work in flood storage areas.To predict the dynamics of incoming floods within a short period of time,The Godunov-type finite volume method was used to establish a two-dimensional hydrodynamic numerical model of shallow water.The model had the advantages of adopting unstructured triangular mesh,which could better fit irregular boundaries,and it adopted GPU heterogeneous parallel technology,which effectively solved the problem of slow computation speed of an unstructured network.The model used a limiter to reduce the diffusion and oscillation of second-order precision values.The accuracy of the model simulation was improved effectively by using negative water depth and dry and wet boundary processing techniques.The model was calibrated using multiple dam-break flow experiments and validated with an excellent capability in calculating dry and wet boundaries and static water balance.Flood data from 1998 in the Nenjiang River Basin was used to simulate and calculate flood evolution in the Pangtoupo flood storage area of the Nenjiang River Basin.The results show that the model simulates a storage capacity of 34.9 billion m^(3) for the Pangtoupo flood storage area,with a relative error of 1.7%compared to the measured value,and a flooded area of 1267.27 km^(2),with a relative error of 9.24%compared to the measured value.When different land types in the study area are classified based on roughness coefficients,the simulated storage capacity results of the model approach to the measured values.The parallelized program improves the model′s calculation speed by 33%.The model thus can rapidly and accurately calculate the flood evolution process of dam-break flows in complex terrain.The results provide relevant information for flood control planning and disaster warning in flood storage areas.