Journal of Computational Physics 150, 17–39 (1999) Article ID jcph.1998.6162, available online at http://www.idealibrary.com on Low-Speed Flow Simulation by the Gas-Kinetic Scheme Mingde Su, ∗ Kun Xu,† and M. S. Ghidaoui‡ ∗ Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, People’s Republic of China; and †Mathematics Department and ‡Department of Civil Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong E-mail: ∗ sumd@mail.tsinghua.edu.cn, †makxu@uxmail.ust.hk, and ‡ghidaoui@usthk.ust.hk Received June 30, 1998; revised December 3, 1998 This paper extends the gas-kinetic BGK-type scheme to low Mach number flows, and thus shows that incompressible flow solutions are accurately obtained from the BGK scheme in the low Mach number limit. The influence of boundary conditions, internal molecular degrees of freedom K , and the flow Mach number M on the ac- curacy of the solutions of incompressible or nearly incompressible flow problems is quantitatively evaluated. The gas-kinetic scheme is tested carefully in two numer- ical examples, namely, the cavity flow problem and the flow passing a backward facing step problem. For the cavity flow problem, the numerical results from the gas- kinetic scheme under different Reynolds numbers compare well with Ghia’s data. For the backward step problem, the numerical results are compared accurately with previously published experimental data. c  1999 Academic Press Key Words: low-speed flow; kinetic scheme; incompressible Navier–Stokes equa- tions. 1. INTRODUCTION Great progress has been achieved in the field of computational fluid dynamics of incom- pressible flows in the past few decades [4, 7]. Despite this success, there remain two main challenges in the numerical solutions of incompressible fluid flows. First, the incompress- ible flow assumption eliminates the unsteady term from the continuity equation and reduces the mass conservation equation to a divergence free velocity field. Therefore, the absence of density from the incompressible fluid flow equations decouples the continuity equation from the momentum and energy equations. Hence, the divergence free velocity field becomes an implicit condition for solving the momentum and energy equations. The enforcement of the divergence free velocity field condition requires the solution of Poisson’s equation for the pressure field. However, for complicated geometry, the Poisson solver is the most time consuming part in the whole flow calculations. The second challenge in the solution of 17 0021-9991/99 $30.00 Copyright c  1999 by Academic Press All rights of reproduction in any form reserved.