Moment-preserving particle merging via non-negative least squares

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.

Figures (19)

• Figure 1: Values of the tail functions $F(500)$ (left) and $F(750)$ (right) as a number of post-merge particles, pre-merge particles with equal weights.
• Figure 2: Standard deviation of the post-merge particle weights (left) and logarithms of the weights (right), pre-merge particles with equal weights.
• Figure 3: Ratio of largest to smallest post-merge weight, pre-merge particles with equal weights.
• Figure 4: Values of the tail functions $F(500)$ (left) and $F(750)$ (right) as a number of post-merge particles, pre-merge particles with unequal weights.
• Figure 5: Standard deviation of the post-merge particle weights (left) and logarithms of the weights (right), pre-merge particles with unequal weights.