  Lifting operators play an important role in starting a kinetic Boltzmann
model from given macroscopic information. The macroscopic variables need to be
mapped to the distribution functions, mesoscopic variables of the Boltzmann
model. A well-known numerical method for the initialization of Boltzmann models
is the Constrained Runs algorithm. This algorithm is used in literature for the
initialization of lattice Boltzmann models, special discretizations of the
Boltzmann equation. It is based on the attraction of the dynamics toward the
slow manifold and uses lattice Boltzmann steps to converge to the desired
dynamics on the slow manifold. We focus on applying the Constrained Runs
algorithm to map density, average flow velocity, and temperature, the
macroscopic variables, to distribution functions. Furthermore, we do not
consider only lattice Boltzmann models. We want to perform the algorithm for
different discretizations of the Boltzmann equation and consider a standard
finite volume discretization.
