Lattice BGK Model for Incompressible Navier–Stokes Equation

Most of the existing lattice Boltzmann BGK models (LBGK) can be viewed as compressible schemes to simulate incompressible fluid flows. The compressible effect might lead to some undesirable errors in numerical simulations. In this paper a LBGK model without compressible effect is designed for simulating incompressible flows. The incompressible Navier–Stokes equations are exactly recovered from this incompressible LBGK model. Numerical simulations of the plane Poiseuille flow, the unsteady 2-D shear decaying flow, the driven cavity flow, and the flow around a circular cylinder are performed. The results agree well with the analytic solutions and the results of previous studies.