Consistent initial conditions for lattice Boltzmann simulations

We propose a simple and effective iterative procedure to generate consistent initial conditions for the lattice Boltzmann equation (LBE) for incompressible flows with a given initial velocity field u0. Using the Chapman-Enskog analysis we show that not only the proposed procedure effectively solves the Poisson equation for the pressure field p0 corresponding to u0, it also generates at the same time the initial values for the nonequilibrium distribution functions {fα} in a consistent manner. This procedure is validated for the decaying Taylor–Green vortex flow in two dimensions and is shown to be particularly effective when using the generalized LBE with multiple relaxation times.