Skip to main content# An Efficient Algorithm for Operating on Large Numbers of Aggregate Particles with Applications to Simulating the Dynamics of Irregularly Shaped Grains

### Presentation #104.02 in the session “Main Belt Asteroids 2: Physical Properties”.

Published onOct 26, 2020

An Efficient Algorithm for Operating on Large Numbers of Aggregate Particles with Applications to Simulating the Dynamics of Irregularly Shaped Grains

A successful approach to simulating rubble piles is the discrete element method (DEM), which uses individual (typically spherical) particles to represent the constituent blocks of the rubble pile, with particle properties chosen to mimic bulk properties of real materials, such as angle of repose. Particles that make up real granular materials, however, are most often not spherical. The shapes of real grains make it more difficult for them to slide past one another, can create quasi-stable equilibria when grains are vertically stacked, and cause granular media to “bulk” under shear (creating more void space and less efficient packing). The aim of our work is to develop a new algorithm for handling simulations using large numbers of irregularly shaped particles with pkdgrav, a DEM code that has been used effectively to model granular dynamics on rubble piles, and show that simulations with irregularly shaped grains can lead to results more akin to real granular systems.

We construct irregular particles by “gluing” spheres together to make bonded (rigid) aggregates. An inefficiency existed in our previous routine for handling these aggregates when their number was similar to the total number of particles (N) because operations involving searches for paricles in aggregates scaled as O(N^{2}). This is prohibitively expensive for processes requiring large N. We solve this inefficiency by putting particles in aggregate order (instead of the order imposed during domain decomposition for parallel gravity calculation), permitting binary searches and a cache line that reduce the scaling to O(N log N) in the worst case, and O(N) in the best. Preliminary tests show a 25–50% decrease in runtime for simulations of several thousand particles using this new algorithm, with better scaling than expected at higher resolution.

To show the importance of modeling irregularly shaped granular material, we apply our method to simulations of the brazil-nut effect (BNE): a mechanism for the vertical migration of boulders in a granular medium that has been suggested as an explanation for exposed boulders on asteroid surfaces. In granular dynamics, the BNE occurs when frictional interactions between particles in a granular medium cause larger blocks to rise to the surface when the medium is subjected to repeated shaking (like brazil nuts rising to the top of a shaken jar of mixed nuts). Our preliminary results show that, when simulating with irregular grains, interparticle friction makes the BNE less efficient and thus the brazil nut rises slower, in contrast with results of simulations using spherical grains.