A higher order moment preserving reduction scheme for the Stochastic Weighted Particle Method

TL;DR

This paper introduces an advanced particle reduction scheme for the Stochastic Weighted Particle Method that preserves higher-order moments and heat flux, improving accuracy and efficiency in simulating the Boltzmann equation.

Contribution

The paper presents a novel reduction scheme that preserves all moments up to second order and heat flux, enhancing the accuracy of the SWPM without increasing computational cost.

Findings

Preserves all velocity moments up to second order.

Accurately computes scalar fourth-order moments at reduced cost.

Improves the efficiency of the SWPM in kinetic simulations.

Abstract

The Stochastic Weighted Particle Method (SWPM) is a Monte Carlo technique developed by Rjasanow and Wagner that generalizes Bird's Direct Simulation Monte Carlo (DSMC) method for solving the Boltzmann equation. To reduce computational cost due to the gradual increase in the number of stochastic particles in the SWPM, Rjasanow and Wagner proposed several particle reduction schemes designed to preserve specified moments of the velocity distribution. Here, we introduce an improved particle reduction scheme that preserves all moments of the velocity distribution up to the second order, as well as the raw and central heat flux both within each group of particles to be reduced and for the entire system. Furthermore, we demonstrate that with the new reduction scheme the scalar fourth-order moment can be computed more accurately at a reduced computational cost.