Variance-Reduced Direct Simulation Monte Carlo with the Bhatnagar-Gross-Krook Collision Operator

TLDR: In this article, the Bhatnagar-Gross-Krook (BGK) collision operator is used to reduce the variance of the collision term in the Boltzmann equation.

Abstract: Direct Simulation Monte Carlo (DSMC) is perhaps the most prevalent stochastic method for simulating rarefied gas flows. High‐signal flows (e.g. Mach number greater than 0.1) are efficiently resolved using DSMC; but low‐signal flows require drastically increased statistical sampling. To address this limitation, Al‐Mohssen and Hadjiconstantinou [1] presented a variance‐reduced DSMC algorithm that dramatically improves the signal‐to‐noise ratio of low‐signal flows. This variance reduction is achieved by exploiting a nearby, analytically‐known equilibrium using importance weights. The weights are updated according to rules derived from the Boltzmann equation.The Bhatnagar‐Gross‐Krook (BGK) collision operator is a simplistic approximation of the collision term in the Boltzmann equation that is useful in a number of fields involving particle‐mediated transport. In this work, we show that the BGK collision operator lends itself naturally to the application of variance reduction using weights by allowing the deri...