In this paper, an improved meshless artificial viscosity (AV) method is proposed and combined with the local radial point interpolation method (LRPIM) and the MacCormack method to establish a newly-developed meshless numerical model, which can efficiently and accurately solve wet-dry moving interfaces problems of shallow water flow. As an important model describing shallow water flow, the two-dimensional (2D) shallow water equations (SWEs) are a hyperbolic system of 1st-order nonlinear partial differential equations which have a characteristic of strong gradient. The LRPIM and MacCormack method are adopted to discretize the 2D SWEs spatially and temporally, respectively. Meanwhile, the method of selecting the different shape of support domain in the LRPIM is employed for properly cooperating with the MacCormack method to accurately capture the direction of wave propagation. For eliminating the non-physical oscillation at the discontinuity of shallow water flow, the improved meshless AV form is first presented. Four challenging numerical examples were selected to verify the proposed model by comparing with the other solutions and experimental observations. The results indicate that the proposed method with improved meshless AV can accurately capture the shock waves and efficiently simulate the wet-dry front changes.

本文提出了一种改进的无网格人工粘度（AV）方法，并结合局部径向点插值法（LRPIM）和MacCormack方法建立了新开发的无网格数值模型，可以高效准确地求解干湿浅水流运动界面问题. 作为描述浅水流动的重要模型，二维（2D）浅水方程（SWE）是一阶非线性偏微分方程的双曲系统，具有强梯度的特点。采用 LRPIM 和 MacCormack 方法分别在空间和时间上离散化 2D SWE。同时，采用LRPIM中选择不同形状支持域的方法与MacCormack方法配合，准确捕捉波的传播方向。为了消除浅水流不连续处的非物理振荡，首先提出了改进的无网格AV形式。通过与其他解决方案和实验观察进行比较，选择了四个具有挑战性的数值例子来验证所提出的模型。结果表明，所提出的改进无网格自动驾驶方法可以准确捕获冲击波并有效模拟干湿锋变化。通过与其他解决方案和实验观察进行比较，选择了四个具有挑战性的数值例子来验证所提出的模型。结果表明，所提出的改进无网格自动驾驶方法可以准确捕获冲击波并有效模拟干湿锋变化。通过与其他解决方案和实验观察进行比较，选择了四个具有挑战性的数值例子来验证所提出的模型。结果表明，所提出的改进无网格自动驾驶方法可以准确捕获冲击波并有效模拟干湿锋变化。