Morphodynamic shallow layer equations featuring bed load and suspended sediment with lattice Boltzmann method

Different coupled systems for the shallow water equation, bed elevation, and suspended load equation are proposed until this day. The main differences come from the physical viewpoints, which caused some distinctions in the models. Recently, a coupled shallow water system of equations over an erodible bed has been proposed, in which the water layer, bed morphodynamics, and suspended sediments are interacting with each other. This system possesses a term in the mass conservation equation that couples the water depth and the bed level in the equilibrium distribution function required by lattice Boltzmann method (LBM). In this paper, the main goal is to utilize an advanced LBM to solve this system of equations. Besides solving the bed morphological equation by LBM, another simple and explicit scheme (like LBM) is proposed to investigate the ability of LBM. As the second goal, a practical approach is developed for applying so-called open boundary condition that relaxes the solution onto a prescribed equilibrium flow.