Conservative evaluation of Boltzmann collision integral in discrete ordinates approximation

Within the framework of a discrete ordinates approximation, two conservative methods of evaluation of a Boltzmann collision integral are proposed. The first method, that is partially conservative, preserves density and kinetic momentum, and is based on a decomposition of the velocity subspace on equal cubic cells centered around discrete velocity nodes. The second method is completely conservative, and needs for its construction, the more elaborate projection technique described in the article. Both methods are tested on a numerical example and compared with other known methods. It is demonstrated that a completely conservative method possesses better convergence properties with respect to numbers of discrete ordinates and integration nodes, and is more efficient in a computational aspect.