Controlling the weights of simulation particles: adaptive particle management using k-d trees

TL;DR

This paper introduces an adaptive particle merging method using k-d trees to efficiently manage particle weights in simulations, improving accuracy and computational efficiency without artifacts.

Contribution

It presents a novel pairwise merging technique with probabilistic schemes and k-d tree search for efficient, adaptive particle weight control in simulations.

Findings

K-d trees enable efficient neighbor searches for merging.

Probabilistic merging schemes affect energy and momentum distributions.

The method improves simulation efficiency while maintaining physical accuracy.

Abstract

In particle simulations, the weights of particles determine how many physical particles they represent. Adaptively adjusting these weights can greatly improve the efficiency of the simulation, without creating severe nonphysical artifacts. We present a new method for the pairwise merging of particles. Pairwise merging reduces the number of particles by combining two particles into one. To find particles that are `close' to each other, we use a k-d tree data structure. With a k-d tree, close neighbors can be searched for efficiently, and independently of the mesh used in the simulation. The merging can be done in different ways, conserving for example momentum or energy. We introduce probabilistic schemes, which set properties for the merged particle using random numbers. The effect of various merge schemes on the energy distribution, the momentum distribution and the grid moments is compared.