An acceleration procedure for discrete velocity approximation of the Boltzmann collision operator

In this paper, we investigate a method of realization of the discrete velocity approximation of the Boltzmann collision operator studied by Palczewski, Schneider and Bobylev. For this realization, we propose an acceleration procedure, which reduces the computational complexity of the method. The efficiency of the acceleration procedure is demonstrated through a set of numerical tests, which include space homogeneous relaxation problems and space nonhomogeneous problem of shock wave formation.