  We examine the Galilean invariance of standard lattice Boltzmann methods for
two-phase fluids. We show that the known Galilean invariant term that is cubic
in the velocities, and is usually neglected, is the main source of Galilean
invariance violations. We show that incorporating a correction term can improve
the Galilean invariance of the method by up to an order of magnitude.
Surprisingly incorporating this correction term can also noticeably increase
the range of stability for multi-phase algorithms. We found that this is true
for methods in which the non-ideality is incorporated by a forcing term as well
as methods in which non-ideality is directly incorporated in a non-ideal
pressure tensor.
