A stable, implicit Time Integration Scheme for Discrete Element Method and Contact Problems in Dynamics

Abstract

The field of applications for Discrete Element Method is constantly growing, enabling the simulation of granular matter. However state of the art integration schemes are mostly adopted from other methods, which results in certain drawbacks in either performance and/or accuracy. The most common time integration schemes in Discrete Element Method are explicit algorithms which are conditionally stable, only. Attempts to use implicit schemes usually require evaluation of the right hand side of the equations of motion, i.e. a complete reevaluation of the neighborhood search and contact forces within predictor-corrector iterations. While both are most suitable for simulations of rapid flows, computational efficiency is sacrificed for simulations of dense granular matter. The algorithm presented in this paper is a predictor-corrector scheme using a prediction of the forces, without evaluating the right hand side, to get an implicit estimate for the next time step. This technique enables to speed up particle simulation while using considerably higher time steps. The usage of the algorithm and the correspondent time step control are shown in example problems and accuracy is verified.