A new macroscopic model derived from the Boltzmann equation and the discontinuous Galerkin method for solving kinetic equations

We propose a new macroscopic model derived from the classical nonlinear Boltzmann equation. A set of partial differential equations is obtained easily. The unknowns depend on the time and space coordinates, and are related to the distribution function, which is the unknown of the Boltzmann equation. This new model guarantees the conservation of the mass, momentum and energy. We prove that the set of equations coincides with the system obtained applying the discontinuous Galerkin method to the Boltzmann equation (see A. Majorana, Kinetic and Related models, 4 (2011), 139–151).