A steady-state lattice Boltzmann model for incompressible flows

In this paper, we propose a steady-state lattice Boltzmann equation which is independent of time for steady incompressible flows. On the basis of the steady-state lattice Boltzmann equation, we find a way of modeling some steady-state problems using the lattice Boltzmann model. In further study, we investigate steady-state incompressible flows with the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations for different space scales. By assuming ρ = constant, we obtain the momentum equation for incompressible steady-state flow. The numerical results show that the new method is effective.