An approximation procedure for the Boltzmann equation based on random choices of collision pairs from a fixed velocity set and on discrete velocity models is designed. In a suitable limit, the procedure is shown to converge to the time-discretized and spatially homogeneous Boltzmann equation.
The global solution of the one-dimensional Broadwell model in the interval [1,0], with reflecting boundary conditions at 0, is shown to converge strongly in L1[0,1] to the constant equilibrium solution.