Asymptotic preserving Monte Carlo methods for the Boltzmann equation

We consider some recently developed unconditionally stable numerical scheme s for the Boltzmann equation, called Time Relaxed (TR) schemes. They share the important property of providing the correct fluid dynamic limit. Stabil ity analysis of the schemes is performed, and the A-stability and L-stabili ty of the schemes is studied. Monte Carlo methods based on TR discretizatio ns are briefly reviewed. In particular, first and second order particle sch emes are compared with a hybrid scheme, in which the equilibrium part of th e distribution is described analytically.