In this paper, a lattice Boltzmann (LB) model is proposed for a class of viscous shallow water equations, in which a second-order moment of the source term is applied to recover the viscosity in the governing equation and eliminate the additional errors generated during the Chapman-Enskog analysis. There are three different schemes based on different treatments of the source term. Through numerical simulations of several classical benchmark problems, we find that the second-order moment of the source term can not only improve the accuracy of the LB model, but also ensure the conservation of the system. In addition, the influence of rainfall intensity on shallow water flow is also taken into account, and the results show that present LB model can also accurately study such problems as overland flows.

本文针对一类粘性浅水方程提出了格子Boltzmann（LB）模型，其中使用源项的二阶矩来恢复控制方程中的粘度并消除在计算过程中产生的附加误差。 Chapman-Enskog分析。基于对源术语的不同处理，存在三种不同的方案。通过对几个经典基准问题的数值模拟，我们发现源项的二阶矩不仅可以提高LB模型的精度，而且可以保证系统的保守性。此外，还考虑了降雨强度对浅水流动的影响，结果表明，目前的LB模型也可以准确地研究陆上水流等问题。