Mixed numerical method for bed evolution

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.