Addressing the gas kinetics Boltzmann equation with branching-path statistics.

This article proposes a statistical numerical method to address gas kinetics problems obeying the Boltzmann equation. This method is inspired by Monte Carlo algorithms used in linear transport physics, where virtual particles are followed backwards in time along their paths. The nonlinear character of gas kinetics translates, in the numerical simulations presented here, into branchings of the virtual particle paths. The obtained algorithms have displayed in the few tests presented here two noticeable qualities: (1) they involve no mesh and (2) they allow one to easily compute the gas density at rarefied places of the phase space, for example, at high kinetic energy.