Efficient explicit time integration algorithms for non-spherical granular dynamics on group S(3)

Discrete element method (DEM) is a powerful tool for the dynamic simulation of irregular non-spherical particle systems. The efficient integration of the rotational motions of numerous particles in DEM poses a big challenge. This paper presents six explicit time integration algorithms, comprising three first-order algorithms and three second-order algorithms, for the rotational motions of non-spherical particles based on the theory of unit quaternion group S(3). The proposed algorithms based on Cayley map do not contain any transcendental function and have high efficiency. The numerical examples underscore the superiority of the first-order symplectic Euler Cayley algorithm (SECay) and the second-order central difference Cayley algorithm (CDCay) in terms of both efficiency and accuracy. In the testing cases of granular systems, SECay and CDCay demonstrate approximately 80% reduction in computational time for the time integration part, compared to the improved predictor-corrector direct multiplication method (IPCDM). Therefore, SECay and CDCay emerge as promising tools for non-spherical DEM simulations.