Discrete model collision operators of Boltzmann type

In the present paper we develop a new kind of discrete velocity models to discretize the Boltzmann collision operator. The chosen approach is situated between the macroscopic ansatz of the BGK-Model and the microscopic ansatz of usual discrete velocity models. Beside questions of the solvability and the form of the solutions of the arising optimization problems, the weak convergence of the discrete collision operators to the original operator is proved.