The numerical errors in idealised discrete element method (DEM) simulations are investigated analytically by comparing energy balances applied at the beginning and end of one time-step. This study focuses on the second-order velocity-Verlet integration scheme due to its widespread implementation in DEM codes. The commercial DEM software PFC2D was used to verify the correctness of key results. The truncation errors, which are larger than the round-off errors by orders of magnitude, have a superlinear relationship with both the simulation time-step and the interparticle collision speed. This remains the case regardless of simulation details including the chosen contact model, particle size distribution, particle density or stiffness. Hence, the total errors can usually be reduced by choosing a smaller time-step. Increasing the polydispersity in a simulation by including smaller particles necessitates choosing a smaller time-step to maintain simulation stability and reduces the truncation errors in most cases. The truncation errors are increased by the dissipation of energy by frictional sliding or by the inclusion of damping in the system. The number of contacts affects the accuracy and one can deduce that because 2D simulations contain fewer interparticle contacts than the equivalent 3D simulations, they therefore have lower accrued simulation errors.
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