The phenomenon of pollutant transport is widespread in shallow water bodies, such as rivers, channels, and lakes. Studying pollutant distribution is of paramount significance for water ecosystem conservation. This paper adopts the lattice Boltzmann method (LBM) based on D2Q16 model to simulate the shallow water flow, and D2Q5 model to simulate the pollutant diffusion process. Based on the simulation results, the influence of different spacing ratios, flow velocities, and various arrangements of column groups on the distribution of pollutants behind the columns are investigated. The results show that the spacing ratio between columns has a substantial impact on the distribution of pollutant concentration behind the columns. When the inlet flow velocity is constant, as the column spacing ratio (L/D) increases, the pollutant distribution at each cross-section behind the column becomes more concentrated. When L/D=1.0, the extreme value of pollutant concentration at each cross-section is greater than that under any other L/D. At a fixed column spacing ratio, as the flow velocity increases, the maximum pollutant concentration at various cross-sections behind the columns generally exhibit a decreasing trend. The arrangement pattern of the column groups has a significant impact on the distribution of pollutant concentration behind the columns, with a lower pollutant concentration behind the columns in square arrangement than in cloverleaf, trapezoidal, and diamond arrangements.