Modelling open-channel flow with rigid vegetation based on two-dimensional shallow water equations using the lattice Boltzmann method

A two-dimensional lattice Boltzmann model with a D2Q9 lattice arrangement is developed to simulate the flow-vegetation interactions in an open channel. The rigid vegetation is modelled as vertical cylinders. A formula of drag force induced by the rigid vegetation is included in the momentum equations as a sink term. The large eddy simulation technique is adopted to simulate turbulent flows. External forces, such as bed friction and drag force, are discretised with a centred scheme. The mixed scheme of no-slip and slip boundary conditions is considered to correctly describe the interaction between the fluid and the boundary wall. The proposed lattice Boltzmann model was used to simulate two experimental results in partially vegetated channels. The results show that the presented model can simulate the vegetated channel flows correctly.