A new consistent discrete-velocity model for the Boltzmann equation.

Journal article, 2002

A discrete velocity model (DVM) of the Boltzmann equation based on a suitable transformation (Carleman transform) of the velocity variables in the collision integral is introduced. The convergence of the discrete collision sums to the Boltzmann operator and convergence of solutions of the DVM to solutions of the Boltzmann equation are then proven in a three-dimensional velocity space. In the space-homogeneous case, a numerical example compares the solutions to the DVM with the exact solution of the Boltzmann equation