A Convergence Proof for Nanbu’s Simulation Method for the Full Boltzmann Equation

Abstract

It is shown that the discrete measures given by the Nanbu simulation method converge with respect to the weak topology of measures to solutions of the Boltzmann equation. The main conditions for this result are that the Cauchy problem for the Boltzmann equation has a sufficiently smooth solution and that the discretization parameters (cell size, timestep and test particle number) satisfy suitable constraints.