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We propose a new deterministic numerical model, based on the discontinuous Galerkin method, for solving the nonlinear Boltzmann equation for rarefied gases. A set of partial differential equations is derived and analyzed. The new model guarantees the conservation of the mass, momentum and energy for homogeneous solutions. We avoid any stochastic procedures in the treatment of the collision operator of the Boltzmamn equation.

A numerical model of the Boltzmann equation related to the discontinuous Galerkin method