An Alternative Lattice Boltzmann Model for Incompressible Flows and Its Stabilization (Communications in Computational Physics, 2018)
In this paper, an alternative lattice Boltzmann (LB) model for incompressibleflows is proposed. By modifying directly the moments of the equilibrium distributionfunction (EDF), the continuous expression of the EDF in tensor Hermite polynomialsis derived using the moment expansion and then discretized with the discrete velocityvectors of the D2Q9 lattice. The present model as well as its counterpart, the incompressibleLB model proposed by Guo, reproduces the incompressible Navier-Stokes(N-S) equations for both steady and unsteady flows. Besides, an alternative pressureformula, which represents the pressure as the diagonal part of the stress tensor, isadopted in the present model. Furthermore, in order to enhance the stability of thepresent LB model, an additional relaxation time pertaining to the non-hydrodynamicmode is added to the BGK collision operator. The present LB model is validated bytwo benchmark tests: the cavity flow with different Reynolds number (Re) and theflow past an impulsively started cylinder at Re=40 and 550.