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

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.

颗粒形状对多数颗粒体系的行为特性具有重要影响。这使得学界对离散元法（discrete element method, DEM）模拟中任意形状颗粒的表征方法产生了日益浓厚的研究兴趣。本文提出一种基于球谐函数（spherical harmonics）表征颗粒形状的模拟方法，该方法可在球坐标系下计算颗粒半径。本文采用了基于相互作用颗粒间重叠体积的能量守恒接触模型。接触检测借助相互作用颗粒的包围球（bounding spheres）实现，这简化了其在传统基于球体的DEM代码中的集成过程。重叠体积及其他所需物理量的计算，通过对包围球所形成的球冠（spherical cap）执行高斯求积积分（Gaussian quadrature integration）完成。随着求积点数的增加，算法的精度与计算成本均会随之提升。该算法已作为LAMMPS用户包得以实现，并通过能量守恒性验证了其正确性。本文还展示了该方法的性能与并行扩展性，并讨论了因重叠体积计算引发的负载不均衡所导致的观测到的扩展性限制。