The lack of Galilean
invariance appears in the equations of motion through the factor 
.
There are Galilean invariant models in which 
. This is
achieved in the FHP model
by changing the probability with which a rest particle is created and
destroyed [19] or by adding a large number of extra rest
particles [18]. Scaling techniques can also be used to eliminate
the lack of Galilean invariance, see section 3.6,
for a single species model. Whichever method is used to
restore Galilean
invariance the model must be run at a constant density.
Galilean invariant models have the disadvantage that they
achieve g = 1 by relaxing semi-detailed balance which is assumed in
the derivation of the equilibrium distribution function.