Effect of the integration scheme on the rotation of non-spherical particles with the discrete element method

The discrete element method (DEM) is an emerging tool for the calculation of the behaviour of bulk materials. One of the key features of this method is the explicit integration of the motion equations. Explicit methods are rapid, at the cost of a limited time step to achieve numerical stability. Fir...

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Vydáno v:	Computational particle mechanics Ročník 6; číslo 4; s. 545 - 559
Hlavní autoři:	Irazábal, Joaquín, Salazar, Fernando, Santasusana, Miquel, Oñate, Eugenio
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Cham Springer International Publishing 01.10.2019 Springer Nature B.V
Témata:	Algorithms Classical and Continuum Physics Computational Science and Engineering Computing time Discrete element method Engineering Equations of motion Exact solutions Inertial reference systems Multiplication Numerical stability Rotating spheres Runge-Kutta method Taylor series Tensors Theoretical and Applied Mechanics Non-spherical particles Discrete element method Granular material Clusters of spheres Explicit rotational integration
ISSN:	2196-4378, 2196-4386
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Shrnutí:	The discrete element method (DEM) is an emerging tool for the calculation of the behaviour of bulk materials. One of the key features of this method is the explicit integration of the motion equations. Explicit methods are rapid, at the cost of a limited time step to achieve numerical stability. First- or second-order integration schemes based on a Taylor series are frequently used in this framework and shown to be accurate for the translational and rotational motion of spherical particles. However, they may lead to relevant inaccuracies when non-spherical particles are used since the orientation implies a modification in the second-order inertia tensor in the inertial reference frame. Specific integration schemes for non-spherical particles have been proposed in the literature, such as the fourth-order Runge–Kutta scheme presented by Munjiza et al. and the predictor–corrector scheme developed by Zhao and van Wachem which applies the direct multiplication algorithm for integrating the orientation. In this work, both methods are adapted to be used together with a velocity Verlet scheme for the translational integration. The performance of the resulting schemes, as well as that of the direct integration method, is assessed, both in benchmark tests with analytical solution and in real-scale problems. The results suggest that the fourth-order Runge–Kutta and the Zhao and van Wachem schemes are clearly more accurate than the direct integration method without increasing the computational time.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	2196-4378 2196-4386
DOI:	10.1007/s40571-019-00232-5