In this paper we consider the introduction of a body force, in the incompre
ssible limit, into the lattice Boltzmann model. A number of methods are con
sidered and their suitability to our objectives determined. When there is n
o density variation across the fluid, gravity can be introduced in the form
of an altered pressure gradient. This method correctly satisfies the Navie
r-Stokes equation; however, if there is a non-negligible density variation
present (produced by the body force or otherwise) this method becomes less
accurate as the density variation increases and the constant density approx
imation becomes less valid. Three other methods are also considered for app
lication when there is a non-negligible density variation. The equations of
motion satisfied by these models are found up to second order in the Knuds
en number and it is seen that only one of these methods satisfies the true
Navier-Stokes equation. Numerical simulations are performed to compare the
different models and to assess the range of application of each.