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

Initialization of lattice Boltzmann models with the help of the numerical Chapman-Enskog expansion