  We extend the applicability of the numerical Chapman-Enskog expansion as a
lifting operator for lattice Boltzmann models to map density and momentum to
distribution functions. In earlier work [Vanderhoydonc et al. Multiscale Model.
Simul. 10(3): 766-791, 2012] such an expansion was constructed in the context
of lifting only the zeroth order velocity moment, namely the density. A lifting
operator is necessary to convert information from the macroscopic to the
mesoscopic scale. This operator is used for the initialization of lattice
Boltzmann models. Given only density and momentum, the goal is to initialize
the distribution functions of lattice Boltzmann models. For this
initialization, the numerical Chapman-Enskog expansion is used in this paper.
