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The smooth and nonsmooth approaches to the discrete element method (DEM) are examined from a computational perspective. The main difference can be understood as using explicit versus implicit time integration. A formula is obtained for estimating the computational effort depending on error tolerance, system geometric shape and size, and on the dynamic state. For the nonsmooth DEM (NDEM), a regularized version mapping to the Hertz contact law is presented. This method has the conventional nonsmooth and smooth DEM as special cases depending on size of time step and value of regularization. The use of the projected Gauss-Seidel solver for NDEM simulation is studied on a range of test systems. The following characteristics are found. First, the smooth DEM is computationally more efficient for soft materials, wide and tall systems, and with increasing flow rate. Secondly, the NDEM is more beneficial for stiff materials, shallow systems, static or slow flow, and with increasing error tolerance. Furthermore, it is found that just as pressure saturates with depth in a granular column, due to force arching, also the required number of iterations saturates and become independent of system size. This effect make the projected Gauss-Seidel solver scale much better than previously thought.

We consider the application of a nonsmooth discrete element method to geometric design optimization of a balling drum outlet used in production of iron ore balls. The geometric design optimization problem is based on the need for homogeneous flow of balls from the balling drum onto a wide belt conveyor feeding a roller screen (sieve). An outlet with two design variables is investigated and the optimal shape for the given system and production flow is found by exploring the design space with 2000 simulations.

The nonsmooth discrete element method (NDEM) has the potential of high computational efficiency for rapid exploration of large design space of systems for processing and transportation of mineral ore. We present parametrization, verification and validation of a simulation model based on NDEM for iron ore green pellet flow in balling circuits. Simulations are compared with camera based measurements of individual pellet motion as well as bulk behavior of pellets on conveyors and in rotating balling drum. It is shown that the NDEM simulation model is applicable for the purpose of analysis, design and control of iron ore pelletizing systems. The sensitivity to model and simulation parameters is investigated. It is found that: the errors associated with large time-step integration do not cause statistically significant errors to the bulk behavior; rolling resistance is a necessary model component; and the outlet flow from the drum is sensitive to fine material adhering to the outlet creating a thick coating that narrows the outlet gaps.

The effect on the convergence of warm start-ing the projected Gauss-Seidel solver for nonsmoothdiscrete element simulation of granular matter are in-vestigated. It is found that the computational perfor-mance can be increased by a factor 2 to 5.

A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies of the corresponding shape and mass distribution. The method also support particles merging with articulated multibody systems. A model approximation error is defined and used to derive conditions for when and where to apply reduction and refinement back into particles and smaller rigid bodies. Three methods for refinement are proposed and tested: prediction from contact events, trial solutions computed in the background and using split sensors. The computational performance can be increased by 5-50 times for model reduction level between 70-95 %.