Moment-preserving particle merging via non-negative least squares

TL;DR

This paper introduces a particle merging algorithm for rarefied gas dynamics that conserves moments and collision rates, reducing errors in macroscopic quantities during simulations.

Contribution

It presents a novel non-negative least squares based merging method that preserves moments and collision rates in particle simulations.

Findings

Lower merging-induced error in macroscopic quantities

Effective conservation of velocity and spatial moments

Extension to preserve collision rates

Abstract

A novel particle merging algorithm for rarefied gas dynamics simulations is proposed that can conserve arbitrary velocity and spatial moments of the particle distribution via solving a non-negative least squares problem. An extension that preserves both exact and approximate collision rates is also derived. The algorithm is applied to the simulation of several model rarefied gas dynamics problems, where it exhibits noticeably lower merging-induced error in key macroscopic quantities.