Preconditioned lattice-Boltzmann method for steady flows

In this paper we propose a preconditioned lattice Boltzmann (LB) method for steady incompressible flows. For steady flows, the macroscopic equations derived from this LB model are equivalent to those from the standard LB model, but with an improved eigenvalue system. The proposed model can be viewed as an explicit solver for preconditioned compressible Navier-Stokes equations. Linear stability analysis is performed and the results show that the stability of the model is the same as that of the standard LB model for low Mach numbers. The proposed model retains the structure of the standard LB model and, hence, possesses all the advantages. Numerical tests show that the convergence rate can be enhanced as much as an order of magnitude compared to the standard lattice Boltzmann method. The accuracy of the solutions is improved as well.