The two-dimensional shallow water equations (SWEs) are a hyperbolic system of first-order nonlinear partial differential equations which have a characteristic of strong gradient. In this study, a newly-developed numerical model, based on local radial point interpolation method (LRPIM), is adopted to simulate discontinuity in shallow water flows. In order to accurately capture the information of wave propagation, the LRPIM is combined with the split-coefficient matrix (SCM) method to transform the SWEs into a characteristic form and the selection of the direction of local support domain is introduced into the LRPIM. An improved meshless artificial viscosity (MAV) technique is developed to minimize the non-physical oscillations near the discontinuities. Then, the LRPIM and the second-order Runge–Kutta method are adopted for spatial and temporal discretization of the SWEs, respectively. The feasibility and validity of the proposed numerical model are verified by the classical dam-break problem and the mixed flow pattern problem. The comparison of the obtained results with the analytical solution and other numerical results showed that the MAV method combined with LRPIM can accurately capture the shocks and has high accuracy in dealing with discontinuous flow by adding appropriate viscosity to the equations in the discontinuous region.

二维浅水方程（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。在这项研究中，采用新开发的基于局部径向点插值法（LRPIM）的数值模型来模拟浅水流的不连续性。为了准确捕捉波传播信息，LRPIM结合分裂系数矩阵（SCM）方法将SWEs转化为特征形式，并将局部支撑域方向的选择引入LRPIM。开发了一种改进的无网格人工粘度 (MAV) 技术，以最大限度地减少不连续点附近的非物理振荡。然后，LRPIM 和二阶 Runge-Kutta 方法分别用于 SWE 的空间和时间离散化。经典的溃坝问题和混合流型问题验证了所提出的数值模型的可行性和有效性。将所得结果与解析解和其他数值结果进行对比表明，MAV方法结合LRPIM可以准确地捕捉到冲击，通过在不连续区域的方程中加入适当的粘度，在处理不连续流动方面具有较高的精度。