Improved lattice Boltzmann model for incompressible two-dimensional steady flows

An improved lattice Boltzmann model with single time relaxation has been proposed for incompressible two-dimensional (2D) steady flows. In the improved model, the steady-state incompressible Navier-Stokes equations can be recovered in exact form and the density of the fluid becomes an irrelevant invariant, satisfying the requirement of incompressibility. Exact analytical solutions to the distribution functions of the 2D triangular and square lattice Boltzmann models have been obtained for steady plane Poiseuille flow based on the present scheme. Boundary conditions that can be used to recover exactly such analytical solutions in numerical simulations are proposed.