Effect of time step on the accuracy of DEM calculations

Discrete Element Method (DEM) is extensively used to simulate the behaviour of particles in various processing units. This method is based on modelling the forces acting between particles in any contact and consequently calculating the new position of particles. The high number of elements and numerous equations needed have made the required computation time very long even using computers with very fast processors. The required computation time mainly depends on the time step. If the time step is chosen very short, the computation time will significantly increase. On the other hand, if the time step is chosen very long, the simulation will be in error due to not fully observing the contacts. In DEM calculations, the time step is chosen as a fraction of the collision time. In this research, a relationship was proposed between the contact time fraction and the error of simulation. In other words, to select the time step in addition to physical parameters, the accuracy of the simulation was also accommodated in the frequently-used relationships. The simulation error was defined as the relative difference between the initial restitution coefficient and the restitution coefficient obtained after simulation. The required time steps to arrive at the simulation error of 5% were calculated for two common contact force models namely, Hertz-Mindlin and linear spring-dashpot. The simulation was performed for two particles with radius of 3 cm, elasticity modulus of 210 GPa, Poisson's ratio of 0.3 and relative velocity of 0.5 m/s. The required time steps were found to be 2.3 and 0.19 µs for the Hertz-Mindlin and the linear spring-dashpot contact force models, respectively. Results showed that with a scaling-down the modulus from 210 GPa to 2.1 MPa, the required time steps for the Hertz-Mindlin and the linear spring-dashpot contact force models, with an equal simulation error, increased by 100 and 316 times, respectively.