Addressing the gas kinetics Boltzmann equation with branching-path statistics

TL;DR

This paper introduces a novel Monte Carlo-based numerical method for solving the Boltzmann equation in gas kinetics, utilizing branching-path statistics to efficiently handle non-linearities and compute densities in rarefied regions.

Contribution

It presents a new mesh-free, branching-path Monte Carlo algorithm inspired by linear transport physics for solving non-linear gas kinetics problems.

Findings

No mesh required in simulations

Efficient computation of gas density in rarefied phase space

Demonstrated effectiveness through initial tests

Abstract

This article proposes a new statistical numerical method to address gas kinetics problems obeying the Boltzmann equation. This method is inspired from some Monte-Carlo algorithms used in linear transport physics, where virtual particles are followed backwards in time along their paths. The non-linear character of gas kinetics translates, in the numerical simulations presented here, in 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. (2) They allow to easily compute the gas density at rarefied places of the phase space, for example at high kinetic energy.