Large eddy simulation(LES)

based on the lattice Boltzmann equation (LBE)

was used to study the square duct turbulent flow at a shear Reynolds number equal to 300 based on the hydraulic diameter and the friction velocity.The flow field was simulated by the multiple relaxation time lattice Boltzmann equation.The non-closure term after filtering was modeled by the shear improved Smagorinsky sub-grid stress model.To combine the lattice Boltzmann and large eddy simulation

the subgrid scales turbulent viscosity was related to the subgrid-scale relaxation time.Then the effective relaxation times were computed locally.The turbulent statistics quantities

including the mean streamwise velocity

mean second velocity

the root-mean-square velocity and the instantaneous streamwise voriticity on different sections

were computed.The comparison result

with the DNS and experimental data

shows that the LES based on the LBE can be used to study the bounded turbulent flow.