CONSTRAINED RUNS ALGORITHM AS A LIFTING OPERATOR FOR THE ONE-DIMENSIONAL IN SPACE BOLTZMANN EQUATION WITH BGK COLLISION TERM

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. The Constrained Runs (CR) algorithm is used in the 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 CR 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 of the one-dimensional in space Boltzmann equation with the Bhatnagar-Gross-Krook collision term.