where the collisions are performed by a single relaxation time BGK operator
The equilibrium distribution function is
where
is a constant, 
and 
.
This reduces to the isotropic, Galilean invariant, two-dimensional
equilibrium distribution derived in section 4.2.1
when D=2, b=6 and 
.
Using this equilibrium distribution and
equations (4.37)-(4.41) we see that
and
