Modelling of complex-shaped granular particles using spherical harmonics

One of the key challenges in the modeling of granular particles is the realistic representation of their shape and implementation of the associated contact laws. A novel simulation technique using spherical harmonics which extends DEM towards modelling arbitrary shaped particles in LAMMPS, is presented. The shape of these particles is represented using spherical harmonics where their radii can be calculated at spherical coordinates [1]. The interaction between these particles depends on the overlap volume, which follows an energy-conserving contact theory [2]. A contact detection algorithm, based on the bounding spheres of the interacting particles, is developed. The overlap volume and other required quantities are calculated using Gaussian quadrature integration of the spherical cap formed by the bounding spheres. The granularity of particles and subsequent computational requirements can thus be controlled by truncating the number of terms in the spherical harmonic expansion [3]. The number of quadrature points and degree of spherical harmonic expansion are shown to affect the precision and computational cost of the simulation, which increases almost quadratically. A simple MPI parallelization results in a significant reduction in the simulation time. The proposed algorithm developed in the form of a user-package in LAMMPS thus aids in the accurate modelling of the motion of complex-shaped particles.