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 boundar
y conditions, internal molecular degrees of freedom K, and the Row Mach num
ber M on the accuracy of the solutions of incompressible or nearly incompre
ssible flow problems is quantitatively evaluated. The gas-kinetic scheme is
tested carefully in two numerical examples, namely, the cavity flow proble
m 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 probl
em, the numerical results are compared accurately with previously published
experimental data. (C) 1999 Academic Press.