基于动态网格和局部时间步长技术的城市洪涝模型加速方法

Acceleration method of the urban flood model based on the dynamic grid system and local time step technology

二维水动力模型能够模拟洪涝在地表的淹没及演进过程,是城市洪涝防御的关键工具,已得到越来越多的研究与应用。在精细化洪涝过程模拟中,细小的网格单元会显著增加网格数量、减小时间步长,大大降低模型计算效率。使用动态网格控制策略可减少实际参与计算的网格单元数量,使用局部时间步长技术可提高模型计算的平均计算步长。融合动态网格控制策略和局部时间步长技术,在有效单元上采用分级时间步长,可进一步结合两种策略的优势,减少模型计算量,提升二维水动力模型的计算效率。理想溃坝算例测试结果表明:动态网格控制策略在干网格数量多时效果明显,局部时间步长技术在网格尺度差异较大时效果显著。在南岗河流域洪涝模拟算例中,两种算法融合使用,最大可节省计算耗时约60%,能有效应对城市洪涝模拟过程中无效网格单元多、无效计算量大的问题。

[Objective] The two-dimensional(2D) hydrodynamic model can simulate the process of flood inundation and evolution.This model is widely used in flood forecasting.The number of grids and time steps considerably affect the computational efficiency of this model.Various methods have been proposed to improve the computational efficiency of the 2D hydrodynamic model.Some researchers use the dynamic grid strategy to calculate only effective grid cells to reduce the impact of the increased number of grids.Others use the local time step(LTS) technology to decrease the time consumption caused by small time steps.Whether the efficiency of model computation can be improved by combining the advantages of the two strategies requires further research.[Methods] Herein,a hybrid algorithm that combines the dynamic grid strategy and LTS technology is proposed to further improve the model performance based on the self-developed flood simulation model,HydroMPM.Technically,the grid cells that actually assist in the flux calculation are first selected as effective cells.Then,the LTS technology is applied to these cells to further optimize the flux calculation and update strategy.The calculation accuracy and efficiency of the hybrid algorithm are compared and analyzed using an ideal dam break case and a typical flood simulation scenario in the Nangang River basin,Guangdong Province,China.[Results] The dynamic grid strategy can accelerate model computation by computing only the effective grid cells.However,the effective cells actually contain all computation grids when the computation area is completely submerged.In this case,the dynamic grid strategy may lead to a high computation amount and low computation efficiency owing to the dynamic update mechanism on all grid cells.The LTS technology can improve the average time step by hierarchically updating the grid cells.However,the performance of this technology barely depends on the difference in grid scale and flow velocity distribution.The urban flood process often has a scattered distribution of the local inundation area,which is suitable for the application of the dynamic grid strategy.At the same time,local mesh refinement is also required in urban flood simulation.This refinement enables the model to better describe the topographic variation in local waterlogging-vulnerable areas.However,it also leads to a large difference in the maximum time step allowed by different grid scales,which requires the application of the LTS technology.By combining the two strategies,the hybrid dynamic grid and LTS technology can further enhance the model performance.In the ideal dam break case,the hybrid algorithm can reduce computation time by 13.1%-64.8%.In the practical application case of the Nangang River basin,the calculation time can be saved by approximately 60%.[Conclusions] The hybrid algorithm successfully combines the advantages of the original dynamic grid strategy and LTS technology to further accelerate the efficiency of the model computation.However,the performance of this hybrid algorithm varies depending on the application scenarios.If the 2D hydrodynamic model is used to simulate only river floods,estuaries,and other areas,the effect of the dynamic grid strategy may not be obvious.The LTS technology may have a general effect when the grid distribution is uniform and the flow state is stable.The hybrid algorithm can combine the advantages of the two abovementioned algorithms.However,this hybrid algorithm has the inherent shortcomings of the two algorithms.In practical applications,a suitable algorithm should be chosen depending on the specific application scenario to achieve good simulation effect and computing efficiency.