  The central framework of a filtered lattice Boltzmann collision operator
formulation is to remove hydrodynamic moments that are not supported by the
order of isotropy of a given lattice velocity set. Due to the natural moment
orthogonality of the Hermite polynomials, the form of a filtered collision
operator is obtained directly via truncation of the Hermite expansion. In this
paper, we present an extension of the filtered collision operator formulation
to enforce Galilean invariance. This is accomplished by representing
hydrodynamic moments in the relative reference frame with respect to local
fluid velocity. The resulting collision operator has a compact and fully
Galilean invariant form, and it can then be exactly expressed in terms of an
infinite Hermite expansion. Giving a lattice velocity set of specific order of
isotropy, a proper truncation of this expansion can be directly determined.
Higher order terms are retained in the truncation if a higher order lattice
velocity set is used, so that Galilean invariance is attained asymptotically.
The previously known filtered collision operator forms can be seen as a limit
of zero fluid velocity.
