Research on Integration Methods for Particle Position Updating in the Discrete Element Method

The discrete element method (DEM) is widely used to simulate the mechanical behavior of granular materials. Particle motion is governed by Newton’s second law, and position updates rely on numerical integration, whose accuracy and efficiency directly influence both the simulation scale and result reliability. In this study, three integration schemes—Verlet, central difference, and fourth-order Runge–Kutta—were implemented within an existing DEM framework to simulate the packing behavior of particles with varying shapes. Corresponding physical packing experiments were conducted, and numerical results were compared with experimental observations to evaluate differences in packing height, morphology, and process. Results show that the fourth-order Runge–Kutta scheme achieves the highest accuracy, with a packing height error of only 5.72% for spherical particles, albeit at a computational cost roughly 2–3 times that of the central difference scheme, making it suitable for high-precision, complex contact scenarios. In contrast, Verlet and central difference schemes are highly sensitive to particle shape, leading to considerable variation in simulation errors. The central difference approach is recommended for vertical displacement predictions in simple contact conditions, while Verlet is better suited for scenarios involving large instantaneous contact forces.