A well-balanced and positivity-preserving meshless method based on smoothed particle hydrodynamics (SPH) is developed to simulate one-dimensional (1D) and two-dimensional (2D) shallow water (SW) flows in open channels with irregular geometries. A new form of the characteristic equations that govern the water-surface level and water velocity is introduced to specify the numerical inflow/outflow boundary conditions. An additional condition, derived from temporal discretization to determine the time-step size, forces the water depth to be positive. A 1D finite volume shallow water (FVSW) model based on the first-order Godunov upwind method is built to conduct a comparison of the 1D meshless-based and mesh-based SW models. Six benchmark cases – still water, single trapezoidal and rectangular and prismatic and non-prismatic channels, and a dendritic channel network – are employed to validate the proposed models and compared with the exact and mesh-based numerical solutions. A real-world case of the Chicago Area Waterways System (CAWS) is investigated to highlight the performance of the proposed 1D model for a practical hydraulic system.

开发了一种基于平滑粒子流体动力学 (SPH) 的平衡良好且保持正性的无网格方法，以模拟具有不规则几何形状的明渠中的一维 (1D) 和二维 (2D) 浅水 (SW) 流动。引入了一种新形式的控制水面水平和水速的特征方程来指定数值流入/流出边界条件。从时间离散化得出的附加条件用于确定时间步长，迫使水深为正。建立了基于一阶 Godunov 迎风法的一维有限体积浅水 (FVSW) 模型，对基于一维无网格和基于网格的 SW 模型进行比较。六个基准案例——静水、单梯形和矩形以及棱柱形和非棱柱形通道，和树枝状通道网络——用于验证所提出的模型，并与精确的和基于网格的数值解进行比较。对芝加哥地区水道系统 (CAWS) 的真实案例进行了研究，以突出实际液压系统所提出的一维模型的性能。