Low-variance Monte Carlo Solutions of the Boltzmann Transport Equation

TL;DR

This paper introduces a variance-reduced stochastic particle method for solving the Boltzmann transport equation, significantly improving efficiency when simulating small deviations from equilibrium in dilute gases.

Contribution

The paper presents a novel variance reduction technique that simulates only deviations from equilibrium, enabling efficient computation for small deviations in the Boltzmann equation.

Findings

Method achieves computational cost independent of deviation size.

Significant efficiency gains over traditional methods for small deviations.

Applicable to various fields with relaxation-time models.

Abstract

We present and discuss a variance-reduced stochastic particle method for simulating the relaxation-time model of the Boltzmann transport equation. The present paper focuses on the dilute gas case, although the method is expected to directly extend to all fields (carriers) for which the relaxation-time approximation is reasonable. The variance reduction, achieved by simulating only the deviation from equilibrium, results in a significant computational efficiency advantage compared to traditional stochastic particle methods in the limit of small deviation from equilibrium. More specifically, the proposed method can efficiently simulate arbitrarily small deviations from equilibrium at a computational cost that is independent of the deviation from equilibrium, which is in sharp contrast to traditional particle methods.