A generalized reduction scheme for the Stochastic Weighted Particle Method

Abstract

The Stochastic Weighted Particle Method (SWPM) of Rjasanow and Wagner is a generalization of the Direct Simulation Monte Carlo method for computing the probability density function of the velocities of a system of interacting particles for applications that include rarefied gas dynamics and plasma processing systems. Key components of a SWPM simulation are a particle grouping technique and particle reduction scheme. These are periodically applied to reduce the computational cost of simulations due to the gradual increase in the number of stochastic particles. A general framework for designing particle reduction schemes is introduced that enforces the preservation of a prescribed set of moments of the distribution through the construction and explicit solution of a system of linear equations for particle weights in terms of particle velocities and the moments to be preserved. This framework is applied to preserve all moments of the distribution up to order three. Numerical simulations are performed to verify the scheme and quantify the degree to which even higher-order moments and tail functionals are preserved. These results reveal an unexpected trade off between the preservation of these higher-order moments and tail functionals.