Conservative energy discretization of Boltzmann collision operator

The paper deduces a kinetic model obtained introducing a discretization of the Boltzmann equation based on an equispaced distribution of allowed particle energies. The model obtained is a system of integro-differential equations with integration over suitable angular variables: one over the portion of the unit sphere between two parallels symmetric with respect to the equatorial plane perpendicular to the velocity of the field particle, and one over a unit circle. The model preserves mass, momentum and energy. Furthermore, there exists an $H$-functional describing trend toward an equilibrium state described by a Gaussian distribution. Particular attention is paid to the identification of a criterion which indicates the values of the discretization parameters.