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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Veröffentlicht in:Computational particle mechanics Jg. 6; H. 4; S. 545 - 559
Hauptverfasser: Irazábal, Joaquín, Salazar, Fernando, Santasusana, Miquel, Oñate, Eugenio
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.10.2019
Springer Nature B.V
Schlagworte:
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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Zusammenfassung: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.
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ISSN:2196-4378
2196-4386
DOI:10.1007/s40571-019-00232-5