基于CUDA架构的内涝一维/二维耦合模型求解方法

Calculation Method of Urban Flooding One-dimensional/Two-dimensional Coupling Model Based on CUDA-based Parallel Implementation

以二维浅水方程为基础建立二维水动力模型,并利用二阶Godunov格式有限体积法进行求解,从而获得地表二维水动力模型的求解模块。将其与SWMM5.1一维水动力模型进行耦合,实现一维、二维水动力模型的耦合模拟。为了提高耦合模型的求解效率,将CUDA并行计算架构引入耦合模型求解过程中。将一维水动力模型的求解过程在主机端运行,将二维水动力模型的求解过程在设备端运行。利用cudaMemcpy函数实现一维、二维模型之间地面水深数据交换,并利用地面水深数据进行一维、二维模型之间双向流量数值的计算,从而实现一维、二维模型的耦合。通过实际案例验证表明,CUDA并行计算架构的引入可以在计算效率方面较非并行求解方法提升6~8倍,计算误差方面可以保证水量平衡相对误差小于0.1%,积水深度误差小于0.01 m。该方法可以用于城市内涝风险评估及排水系统规划等场合。

A two-dimensional(2D)hydrodynamic model was built based on the shallow water equation.The equation was then solved by using a second order Godunov-type scheme,and the solution module of the 2D surface hydrodynamic model was obtained.The 2D hydrodynamic module was coupled with SWMM5.1 one-dimensional(1D)hydrodynamic model,and coupling simulation of 1D and 2D hydrodynamic models was realized.In order to improve the solution efficiency of the coupling model,CUDA-based parallel implementation was introduced into the solution process.Solution process of the 1 D hydrodynamic module was ran on the host side,and the 2D hydrodynamic module was ran on the device side.Exchange of surface water depth data between 1 D and 2 D models was realized by using cudaMemcpy function,and water volume exchange between 1 D and 2 D models was calculated according to the surface water depth,so that coupling of the 1 D and 2 D models was achieved.Tested by a real study case,introduction of CUDA-based parallel implementation improved the solution efficiency by 6 to8 times compared with non-parallel solution,and the relative error of water balance was less than 0.1%and the error of water depth was less than 0.01 m.Therefore,the calculation method can be used in cases such as risk assessment of urban flooding and storm water drainage system planning.