The morphological evolution in shallow water flows was investigated in this study. The shallow water equations were solved for the flows using the lattice Boltzmann method with multiple-relaxation time and an improved scheme for the momentum source terms in which the bed elevation gradients were included. The fifth-order Euler-WENO scheme was coupled with the lattice Boltzmann method to solve the Exner equation for the bed evolution caused by bed-load sediment transport. Five typical test cases were simulated by the coupled model and the numerical results agreed well with either the corresponding experimental data or the analytical solutions. This suggests that the present model has great potential to predict morphological change in shallow water flows. Furthermore, the effect of different values of time step for morphodynamic evolution and flow field were studied and no obvious difference was produced for these two kinds of method in the range tested in the present study.

As for the level of tail-water often rose when the situation of tailrace river changing during the process of construction of hydroelectric power station, one-dimensional mathematical model is used through two procedures to solve this problem. In the first, the sensitivity of three key parameters including roughness, cross-section spacing Δs, starting regulation level and section in the mathematical model were discussed. The results indicate that: (1) Positive relationship between ΔY/Y and n, shows the greater flow rate, the more sensitive of water depth changes to roughness coefficient; (2) The cross-section spacing Δs affect the large flow more obvious than the smaller; (3) The effect of the middle and lower reaches of river are bigger than the upstream. Research results provided guidance of model parameters selection.