Spherical harmonic–based DEM in LAMMPS: Implementation, verification and performance assessment

Abstract

Particle shape plays a major role in the behaviour of most granular systems. This has led to increasing interest in the representation of arbitrarily shaped particles in discrete element method (DEM) simulations. In this paper, we present a simulation approach based on the representation of particle shapes using spherical harmonics where their radii can be calculated in spherical coordinates. An energy-conserving contact model is adopted which is based on the volume of overlap between interacting particles. Contact detection makes use of the bounding spheres of the interacting particles, simplifying its incorporation within a conventional sphere-based DEM code. The volume of overlap and other required quantities are calculated using Gaussian quadrature integration of the spherical cap formed by the bounding spheres. Both the accuracy and the computational cost increase with the number of quadrature points. The algorithm has been implemented as a LAMMPS user package, and verified by means of energy conservation. The performance and parallel scaling of the approach are illustrated, and an observed scaling limitation owing to load imbalance arising from the evaluation of the overlap volume is discussed.

Program summary

Program Title: SH-DEM LAMMPS package

CPC Library link to program files: https://doi.org/10.17632/vk6fj6yjtf.1

Developer's repository link: https://github.com/EPCCed/lammps/tree/feature-sh-dem

Licensing provisions: GPLv2

Programming language: C++

Nature of problem: Particles are often highly non-spherical. Spherical harmonics provide a natural way to represent complex particle shapes within a discrete element method (DEM) simulation. However, there is no publicly available DEM code which allows particle shapes to be represented using spherical harmonics.

Solution method: The SH-DEM package extends the capabilities of LAMMPS so that irregularly shaped particles can be represented using spherical harmonics. The package includes the definition of a new ‘shdem’ atom style for spherical harmonic particles, a time integration scheme for these particles based on the Velocity Verlet algorithm, algorithms for detecting and evaluating contacts between spherical harmonic particles, evaluation of the contact forces between these particles and rigid walls, and two energy computes for groups of spherical harmonic particles.

Additional comments including restrictions and unusual features: The SH-DEM package is applicable only to 3D simulations. In order for a particle to be defined by spherical harmonics, it is required that any line segment drawn from an origin inside the particle crosses the contour of the particle's three-dimensional surface only once. If the ‘shdem’ atom style is used, the current implementation requires all particles to be defined using this atom style, e.g., mixtures of sphere and shdem atom styles are not permitted.