On the central difference algorithm in discrete element modelling of impact

The paper provides a comprehensive analysis of the accuracy and stability of the central difference scheme when applied to simulate a simple impact problem in the context of the discrete element approach. It is revealed that the algorithm exhibits some different behaviour due to the inherent nonlinearity/ discontinuity of the impact system. Particularly, for an elastic or slightly inelastic impact, the stable/unstable region governing the selection of a maximum time step size is essentially different from that defined by the conventional linear stability criterion, and thus a smaller time step should be employed in order to reduce the possible occurrence of an unexpected numerical instability