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A Hybrid Algorithm of Event-Driven and Time-Driven Methods for Simulations of Granular Flows

Published online by Cambridge University Press:  20 August 2015

Jun Huang  and
Ole Jørgen Nydal
Jun Huang*
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim, Norway
Ole Jørgen Nydal*
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim, Norway
*
Corresponding author.Email:[email protected]
Email:[email protected]
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Abstract

The classical discrete element approach (DEM) based on Newtonian dynamics can be divided into two major groups, event-driven methods (EDM) and time-driven methods (TDM). Generally speaking, TDM simulations are suited for cases with high volume fractions where there are collisions between multiple objects. EDM simulations are suited for cases with low volume fractions from the viewpoint of CPU time. A method combining EDM and TDM called Hybrid Algorithm of event-driven and time-driven methods (HAET) is presented in this paper. The HAET method employs TDM for the areas with high volume fractions and EDM for the remaining areas with low volume fractions. It can decrease the CPU time for simulating granular flows with strongly non-uniform volume fractions. In addition, a modified EDM algorithm using a constant time as the lower time step limit is presented. Finally, an example is presented to demonstrate the hybrid algorithm.

Keywords

70F0565K0574S3070F10Time-driven method (TDM)event-driven method (EDM)Hybrid algorithm of event-driven and time-driven methods (HAET)granular flow
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 4 , October 2011 , pp. 1027 - 1043
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Jaeger, H. M., Nagar, S. R. and Behringer, R. P., Granular solids, liquids, and gases, Rev. Mod. Phys., 68 (1996), 1259–1273.CrossRefGoogle Scholar
[2]Forterre, Y. and Pouliquen, O., Flows of dense granular media, Annu. Rev. Fluid Mech., 40 (2008), 1–24.CrossRefGoogle Scholar
[3]Hogue, C. and Newland, D., Efficient computer simulation of moving granular particles, Power Tech., 78 (1994), 51–66.CrossRefGoogle Scholar
[4]Dziugys, A. and Peters, B., Anapporachtosimulate the motion of spherical and non-spherical fuel particles in combustion chambers, Granular Matter, 3 (2001), 231–265.CrossRefGoogle Scholar
[5]Johnson, P. C. and Jackson, R., Frictional-collision consititutive relations for granular materials with application relations to plane shearing, J. Fluid Mech., 176 (1987), 67–93.CrossRefGoogle Scholar
[6]Compbell, C. S., Rapid granular flow, Annu. Rev. Fluid Mech., 22 (1990), 57–92.Google Scholar
[7]Parram, J. W., Wertheim, M. S., Lebowirz, J. L. and Williams, G. O., Monte Carlo simulations of hard spheroids, Chem. Phys. Lett., 105 (1984), 277–280.Google Scholar
[8]Cundall, P. A. and Strack, O. D. L., A discrete numerical model for granular assemblies, Geotechnique, 29 (1979), 47–65.CrossRefGoogle Scholar
[9]Ramirez, R., Pøschel, T., Brilliantov, N. V. and Schwager, T., Coefficient of restitution of colliding viscoelastic spheres, Phys. Rev. E, 60 (1999), 4465–4472.Google Scholar
[10]Hertz, H., Uber die Beruhrung fester elasticher Korper, J. Reine Angew. Math., 92 (1882), 156–171.Google Scholar
[11]Johnson, K. L., Contact Mechanics, Cambridge University, 1982.Google Scholar
[12]Kuwabara, G. and Kono, K., Resitution coefficient in a collision between two spheres, Jpn. J. Appl. Phys., 26 (1987), 1230–1233.Google Scholar
[13]Mindlin, R. D., Compliance of elastic bodies in contact, J. Appl. Mech., 16 (1949), 259–268.Google Scholar
[14]Huang, Y. J., Chan, C. K. and Zamankhan, P., Granular jet impingement on a fixed target, Phys. Rev. E, 82(3) (2010), 031307.Google Scholar
[15]Ji, S. and Shen, H. H., Effect of contact force models on granular flow dynamics, J. Eng. Mech., 11 (2006), 1252–1259.Google Scholar
[16]Shen, H. H. and Sankaran, B., Internal length and time scales in a simple shear granular flow, Phys. Rev. E, 70 (2004), 051308.Google Scholar
[17]Babic, M., Shen, H. H. and Shen, H. T., The stress tensor in granular shear flows of uniform, deformable disks at high solids concentrations, J. Fluid Mech., 219 (1990), 81–118.CrossRefGoogle Scholar
[18]Allen, M. P. and Tildesley, D. J., Computer Simulation of Liquids, Oxford University, 1987.Google Scholar
[19]Zamankhan, P. and Huang, J., Complex flow dynamics in dense granular flow, part II: simulation, J. Appl. Mech., 74 (2007), 691–702.CrossRefGoogle Scholar
[20]Lun, C. K. K. and Bent, A. A., Numerical simulation of inelastic frictional spheres in simple shear flow, J. Fluid Mech., 258 (1994), 335–353.Google Scholar
[21]Maw, N., A Theoretical and Experimental Investigation into the Impact and Rebound of Elastic Bodies, PhD thesis, Sunderland Polytechnic U.K, 1976.Google Scholar
[22]Zamankhan, P. and Bordbar, M. H., Complex flow dynamics in dense granular flow, part I: experiment, J. Appl. Mech., 73 (2006), 648–657.Google Scholar
[23]Goldsmith, W., Impact: The Theory and Phycisal Behavior of Colliding Solid, Edward Arnold, 1960.Google Scholar
[24]Verlet, L., Computer experiments on classical fluids I: thermodynamical properties of Lennard-Jones molecules, Phys. Rev., 159 (1967), 98–103.Google Scholar
[25]Quentrec, B. and Brot, C., The potential calculation and some application, J. Comput. Phys., 13 (1975), 430–432.Google Scholar
[26]Amarouchene, Y., Boudet, J. F. and Kellay, H., Dynamics and sand dunes, Phys. Rev. Lett., 86 (2001), 4286–4289.Google Scholar
[27]Buchholtz, V. and Poschel, T., Interaction of a granular stream with an obstacle, Granular Matter, 1 (1998), 33–41.CrossRefGoogle Scholar
[28]Wassgrena, C. R., Cordova, J. A., Zenit, R. and Karion, A., Dilute granular flow around an immersed cylinder, Phys. Fluids, 15 (2003), 3318–3330.Google Scholar
[29]Nedderman, R. M., Statics and Kinematics of Granular Materials, Cambridge University Press, London, 1992.CrossRefGoogle Scholar
[30]Hou, M., Chen, W., Zhang, T., Lu, K. and Chan, C. K., Globeal nature of dilute-to-dense transition of granular flow in a 2-D Channel, Phys. Rev. Lett., 91 (2003), 204301.Google Scholar
[31]Midi, G. D. R., On dense granular flows, Eur. Phys. J. E, 14 (2004), 341–365.Google Scholar
[32]Arfken, G. B. and Weber, H. J., Mathematical Methods for Physicsists (Internaional Edition), 6 Ed., Elsevier, 2005.Google Scholar