The initial approach to simulating a boundary was to follow the FHP
method and reflect all distribution functions, at the boundary sites, back
along the links they arrived on. Averaging the velocity
at the boundary, before and after a collision,
gives the required boundary condition
. Further consideration
of this method [21] has shown that sites adjacent to the boundary
sites `see' a flow at the boundary with the same magnitude but opposite
direction. It is pointed out by Cornubert et al. [21] that this
form of boundary collision can better simulates a no-slip boundary at the
centre of the links, half way between a boundary site and an adjacent
non-boundary site. The bounce back boundary collisions were further
modified by Ziegler [49]
who considered the boundary to be coincident with
the boundary sites. At these boundary sites, after the propagation, the
distribution functions on the links interior to the boundary are set equal
to the distribution functions on the `opposite' exterior links. The
`opposite' link being the link in the opposite direction. Thus at a
wall parallel to the direction 
, as in
figure 3-6, the distribution function approaching the boundary
on link 
(interior to the wall) is set equal
to the distribution function 
(exterior to the wall).
These modified boundary conditions are seen to simulate a no-slip
boundary more accurately than the standard bounce back rules
when applied to Poiseuille flow [49]. Bounce back boundary conditions
only give first-order accuracy [21, 50] and it can be shown
[51] that the standard bounce back conditions produce a wall velocity
which is a function of the relaxation parameter 
and is only
zero for 
.