Lattice Bgk Model for Incompressible Navier–Stokes Equation

Journal of Computational Physics 165, 288–306 (2000) doi:10.1006/jcph.2000.6616, available online at http://www.idealibrary.com on

Lattice BGK Model for Incompressible Navier–Stokes Equation
Zhaoli Guo,∗ Baochang Shi,† and Nengchao Wang†
∗ National Laboratory of Coal Combustion, and Department of Computer Science, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China; and †Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China E-mail: [e-mail] Received May 10, 1999; revised February 28, 2000

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. c 2000 Academic Press Key Words: Lattice BGK method; Incompressible Navier–Stokes equation.

1. INTRODUCTION

The Lattice Boltzmann BGK (LBGK) method is a new numerical scheme for simulating viscous compressible flows in the subsonic regime [2]. In recent years, LBGK has achieved great success in simulations of fluid flows and in modeling physics in fluids. Through multiscaling expansion [7], the compressible Navier–Stokes equations can be recovered from the lattice Boltzmann BGK equation on the assumptions that (i) the Mach number is small, and (ii) the density varies slowly. Therefore, theoretically the LBGK model can only be used to simulate compressible flows in the incompressible limit.

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