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.

Automated summary

This article proposes a statistical numerical method for addressing gas kinetics problems based on the Boltzmann equation. Inspired by Monte Carlo algorithms used in linear transport physics, this method tracks virtual particles backwards in time along their paths. The nonlinear nature of gas kinetics is represented in the numerical simulations by branching of virtual particle paths.