Computers and Chemical Engineering 49 (2013) 183–193 Contents lists available at SciVerse ScienceDirect Computers and Chemical Engineering jo u rn al hom epa ge : www.elsevier.com/locate/compchemeng Assessment of the potentials of implicit integration method in discrete element modelling of granular matter K. Samiei a , B. Peters a,∗ , M. Bolten b , A. Frommer b a Research Group in Engineering Science, Faculty of Science, Technology and Communication, University of Luxembourg, L-1359 Luxembourg City, Luxembourg b Department of Mathematics, Faculty C-Mathematics and Natural Sciences, University of Wuppertal, D-42097 Wuppertal, Germany a r t i c l e i n f o Article history: Received 22 May 2012 Received in revised form 25 August 2012 Accepted 20 October 2012 Available online 3 November 2012 Keywords: Implicit integration DEM Numerical analysis Granular material a b s t r a c t Discrete element method (DEM) is increasingly used to simulate the motion of granular matter in engi- neering devices. DEM relies on numerical integration to compute the positions and velocities of particles in the next time step. Typically, explicit integration methods are utilized in DEM. This paper presents a systematic assessment of the potentials of implicit integration in DEM. The results show that though the implicit integration enables larger time steps to be used compared to the common explicit methods, the overall speed up is overruled by higher computational costs of the implicit method. © 2012 Elsevier Ltd. All rights reserved. 1. Introduction In order to predict and optimize the behaviour and motion of granular matter in engineering devices, numerical simulation tools are increasingly employed (Cleary, 2004). To date the discrete ele- ment method (also called distinct element method) is the leading approach to simulate the dynamics of granular media. The DEM is a numerical approach where statistical measures of the global behaviour of a phenomenon are computed from the individual motion and mutual interactions of a large population of elements (Cundall & Strack, 1979). Modelling is straightforward: the grains are the elements, they interact through local, pairwise contacts, yet are also subject to external factors such as gravitation or con- tacts with surrounding objects, and they otherwise obey Newtons laws of motion (Kozicki & Donzé, 2009). In contrast to the contin- uum approach, DEM analysis accounts for inter-particle contacts. However, run-time efficiency is still a limiting factor in large scale applications and therefore research and investigation of alternative methods and algorithms and evaluations of their costs and benefits are of grave importance. The Lagrangian time driven method is applied to the discrete particles of a moving ensemble which is regarded as a system of a finite number of visco-elastic particles with a given shape and material properties. The state of particles is obtained by time ∗ Corresponding author. Tel.: +352 466644 5496; fax: +352 466644 5200. E-mail address: bernhard.peters@uni.lu (B. Peters). URL: http://www.xdem.de (B. Peters). integration of the dynamics equations derived from the classical Newtonian mechanics approach based on the Newton’s second law for translation and rotation of each particle in the particle ensemble. All the forces and moments acting on each particle are evaluated at every time step. The state of particles at the next time step can be calculated from the state of particles at the current and/or previous time steps. This will simplify solving the equation because the new positions could be expressed as explicit functions of the already known values. If the state of particles at the next time step is calculated not only from the current and previous time steps but also from the next time step, the equation of motion will be implicit in new positions. Generally the implicit method is computationally more expensive because it requires a system of equations to be solved at each time step. On the other hand, relatively larger time steps could be used in implicit methods due to higher numerical stability. The common practice in DEM simulations is the explicit updating and the use of implicit methods has been very limited. A method called discontinuous deformation analysis (DDA) (Ke & Bray, 1995), was one of the first works presenting an implicit method for two dimensional simulation of particulate media. This method is claimed to solve systems of few thousands of parti- cles in “reasonable times” though no comparison with explicit methods was presented. More recently, Schäfer and Negrut (2010) evaluated the potential of implicit integration methods in molec- ular dynamics simulation of biological molecules. Although they report good energy conservation response by the implicit methods, the increase in the time step was limited due to loss of con- vergence of the iterative method. Tuley, Danby, Shrimpton, and 0098-1354/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compchemeng.2012.10.009