Hybrid Quasi-three-dimensional modeling of morphological processes based on equilibrium sediment transport using Lattice Boltzmann and finite-difference methods

A quasi-three-dimensional model based on the combination of the lattice Boltzmann method and the finite difference method was developed to study morphological processes, based on an equilibrium approach to sediment transport. In this model, the three-dimensional velocity field is obtained by calculating the two horizontal components of the velocity integrated on the vertical using the Lattice Boltzmann method, and then combined with a logarithmic velocity profile. The transport of sediment particles considered is composed of a bed load (Van Rijn 1987) and a suspended load transport rate. The latter is obtained by calculating the equilibrium flow rate of suspended sediments from equilibrium concentrations and logarithmic velocities. The rate of change of the bottom is subsequently obtained from the finite difference resolution of the sediment mass conservation equation. A good agreement with the results of Van Rijn (Van Rijn 1987) was obtained when applying the model to a channel of a constant with and a horizontal bed, and partially closed by a dam.