The governing equations of bed-load sediment transport are the shallow water equations and the Exner equation. To embody the advantages of the lattice Boltzmann method (e.g., simplicity, efficiency), the three-velocity (D1Q3) and five-velocity (D1Q5) double-distribution-function lattice Boltzmann models (DDF-LBMs), which can present the numerical solution for one-dimensional bed-load sediment transport, are proposed here based on the quasi-steady approach. The so-called DDF-LBM means we use two distribution functions to describe the movement of the two components, respectively. By using the Chapman–Enskog expansion, the governing equations can be recovered correctly from the DDF-LBMs. To illustrate the efficiency of these, two benchmark tests are used, and excellent agreements between the numerical and analytical solutions are demonstrated. In addition, we show that the D1Q5 DDF-LBM has better accuracy compared to the Hudson’s method
