基于非均匀网格的高效高精度洪涝过程模拟

随着计算机技术的发展，网格划分技术日趋成熟。针对变化环境下洪涝灾害频发以及实际地形范围广泛，且通常存在狭长沟道与广阔泛洪区等问题，本文建立了一套具有层次拓扑关系的结构化非均匀网格划分模型，并与基于GPU加速的高分辨率数值模型相结合模拟地表水流动过程。高质量网格影响着模型计算精度与计算效率，非均匀网格划分技术以地形高程的梯度变化为基础设计网格划分原则，在需要高分辨率网格的计算域中检测关键地形特征以可靠地求解浅水方程，并可对局部区域网格静态加密，从而在较准确捕获水位计算敏感区的同时减少计算网格数量，降低计算成本。数值模型采用Godunov格式有限体积法进行空间离散，利用TVD-MUSCL格式将模型时间与空间精度提高至二阶，通过GPU并行技术在不降低计算精度基础上大幅提高模型运行速度。使用理想和实际案例来演示基于GPU加速的高分辨率模型在非均匀网格上的流量模拟性能，以较为准确获取洪水淹没时间及淹没面积等信息。结果表明，基于非均匀网格的高分辨率数值模型具有良好的稳定性，与均匀网格相比，在保证模拟精度的前提下，其运行速度约为均匀网格的2-3倍，计算效率在GPU加速基础上进一步提高。新模型适用于模拟复杂区域的大规模洪水演进及城市内涝过程，在实际大尺度洪水模拟中具有一定潜力。

High-efficient and High-precision Flood Process Simulation Based on the Non-uniform Grid

With the development of computer technology, grid division technology is becoming more mature. Considering the frequent occurrence of floods due to climate change, the broad extents of calculation domains, the wide range of actual terrain, and the study area usually has narrow and long gullies and wide flooding areas, this paper proposes a structured non-uniform grid model with hierarchical topological relationships combined with a high-resolution model based on GPU acceleration to simulate the surface water flow process. High-quality grids affect the calculation accuracy and efficiency of the model. The principle of grid division is designed based on the gradient change of terrain elevation, and key terrain features are detected in the computational domain that requires high-resolution grids to reliably solve shallow water equations. Moreover, local area grids can be statically encrypted, so that the sensitive area of the water level calculation can be captured more accurately, while reducing the number of calculation grids and reducing the calculation cost. The numerical model adopts Godunov-type finite volume method for spatial discretization, uses the second-order TVD-MUSCL format to improve the temporal and spatial accuracy of the model, and uses GPU parallel technology to greatly increase the running speed of the model without reducing the calculation accuracy. Demonstrate the flow simulation performance of high-resolution models on non-uniform grids through ideal and practical cases to obtain flood inundation time and inundation area more accurately. The results show that the numerical model based on the non-uniform grid has good stability, compared with the uniform grid, its running speed is about 2-3 times under the premise of ensuring the simulation accuracy and the efficiency is further improved on the basis of GPU acceleration. The new model is suitable for simulating large-scale flood evolution and urban inundation processes in complex areas, which has certain potential in actual large-scale flood simulation.