Skip to main content
Log in

Numerical simulations in granular matter: The discharge of a 2D silo

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

In this paper I give a short and elementary review of numerical simulations in granular assemblies, giving the process of discharge of a 2D silo as an example. The strengths and limitations of different approaches are discussed, together with some comments on the specific issues related to the numerics of discontinuous dissipative collisions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J Duran, Sands, powders and grains (Springer, New York, 2000)

    MATH  Google Scholar 

  2. H M Jaeger and S R Nagel, Rev. Mod. Phys. 68, 1259 (1996)

    Article  ADS  Google Scholar 

  3. P G de Gennes, Rev. Mod. Phys. 71, S374 (1999)

    Article  Google Scholar 

  4. J Kakalios, Am. J. Phys. 73, 8 (2005)

    Article  ADS  Google Scholar 

  5. I Zuriguel, T Mullin and J M Rotter, Phys. Rev. Lett. 98, 028001 (2007)

    Google Scholar 

  6. H A Janssen, Z. Ver. Dtsch. Ing. 39, 1045 (1895); translated to English by M Sperl in arXiv:cond-mat/0511618v1

    Google Scholar 

  7. A J Liu and S R Nagel, Nature (London) 396, 21 (1998)

    Article  ADS  Google Scholar 

  8. A Rosato, K J Strandburg, F Prinz and R H Swendsen, Phys. Rev. Lett. 58, 1038 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  9. R Jullien, P Meakin and A Pavlovitch, Phys. Rev. Lett. 69, 640 (1992)

    Article  ADS  Google Scholar 

  10. T Schnautz, R Brito, C A Kruelle and I Rehberg, Phys. Rev. Lett. 95, 028001 (2005)

    Google Scholar 

  11. M P Ciammarra et al, Phys. Rev. Lett. 96, 058001 (2006)

    Google Scholar 

  12. J S Olafsen and J S Urbach, Phys. Rev. Lett. 81, 4369 (1998)

    Article  ADS  Google Scholar 

  13. J S Olafsen and J S Urbach, Phys. Rev. E60, R2468 (1999)

    ADS  Google Scholar 

  14. X Nie, E Ben-Haim and S Y Chen, Europhys. Lett. 51, 679 (2000)

    Article  ADS  Google Scholar 

  15. N V Brilliantov and T Pöschel, Kinetic theory of granular gases (Oxford Univ. Press, Oxford, 2004)

    MATH  Google Scholar 

  16. M P Allen and D J Tildesley, Computer simulation of liquids (Oxford Univ. Press, Oxford, 1987)

    MATH  Google Scholar 

  17. D Frenkel and B Smit, Undersatanding molecular simulation: From algorithms to applications (Academic Press, San Diego, 2002)

    Google Scholar 

  18. B J Adler and T E Wainwright, J. Chem. Phys. 27, 1208 (1957)

    Article  ADS  Google Scholar 

  19. N V Brilliantov, T Pöschel, W T Kranz and A Zippelius, Phys. Rev. Lett. 98, 128001 (2007)

  20. T Pöschel and T Schwager, Computational granular dynamics (Springer, Berlin, 2005)

    Google Scholar 

  21. S McNamara and W R Young, Phys. Fluids A4, 496 (1992)

    ADS  Google Scholar 

  22. S McNamara and W R Young, Phys. Rev. E50, R28 (1994)

    ADS  Google Scholar 

  23. D C Rapaport, J. Comp. Phys. 34, 184 (1980)

    Article  ADS  Google Scholar 

  24. D C Rapaport, The art of molecular dynamics simulation (Cambridge Univ. Press, Cambridge, 1995)

    Google Scholar 

  25. M Marin, D Risso and P Cordero, J. Comp. Phys. 109, 306 (1993)

    Article  MATH  ADS  Google Scholar 

  26. J J Moreau, Eur. J. Mech. A-Solids 13, 93 (1994)

    MATH  MathSciNet  Google Scholar 

  27. M Jean, Comput. Methods Appl. Mech. Engg. 177, 235 (1994)

    Article  MathSciNet  Google Scholar 

  28. T Unger and J Kertész, in Modeling complex systems: Seventh Granada lectures edited by P L Garrido and J Marro (AIP, New York, 2003)

    Google Scholar 

  29. D E Wolf, in Computational Condensed Mater Physics: Lecture Manuscripts of the 37th Spring School of the Institute of Solid State Research (IFF Ferienkurs, Forschungszentrum Jülich, 2006) vol. 32

    Google Scholar 

  30. J J Moreau, in Nonsmooth/Nonconvex Mechanics with Applications in Engineering, II. NNMAE 2006 edited by C C Baniotopoulos (Ziti, Thessaloniki, 2006)

    Google Scholar 

  31. J Schäfer, S Dippel and D E Wolf, J. Phys. I France 6, 5 (1996)

    Article  Google Scholar 

  32. H Kruggel-Emden et al, Powder Tech. 171, 157 (2007)

    Article  Google Scholar 

  33. T Schwager and T Pöschel, Granular Matter 9, 465 (2007)

    Article  Google Scholar 

  34. N V Brilliantov, F Spahn, J-M Hertzsch and T Pöschel, Phys. Rev. E53, 5382 (1996)

    ADS  Google Scholar 

  35. G Kuwabara and K Kono, Jpn. J. Appl. Phys. 26, 1230 (1987)

    Article  ADS  Google Scholar 

  36. T Schwager and T Pöschel, arXiv:cond-mat/07081434 (2007)

  37. J Lee and H J Herrmann, J. Phys. A26, 373 (1993)

    ADS  Google Scholar 

  38. T Tsuji, T Tanaka and T Ishida, Powder Tech. 71, 239 (1992)

    Article  Google Scholar 

  39. O R Walton and R L Brown, J. Rheol. 30, 949 (1986)

    Article  ADS  Google Scholar 

  40. P A Cundall and O D L Strack, Géotechnique 29, 47 (1979)

    Article  Google Scholar 

  41. L Brendel and S Dippel, Physics of dry granular materials, NATO ASI Series E (1998) vol. 350, p. 313

    Google Scholar 

  42. D Beeman, J. Comput. Phys. 20, 130 (1976)

    Article  ADS  Google Scholar 

  43. K Refson and S Pawley, Mol. Phys. 61, 669 (1987)

    Article  ADS  Google Scholar 

  44. W A Beverloo, H A Leniger and J van de Velde, Chem. Eng. Sci. 15, 260 (1961)

    Article  Google Scholar 

  45. R M Nedderman, U Tüzün, S B Savage and G T Houlsby, Chem. Eng. Sci. 37, 1597 (1982)

    Article  Google Scholar 

  46. Here a silo is any hopper with a flat bottom

  47. K To, P Y Lai and H K Pak, Phys. Rev. Lett. 86, 71 (2001)

    Article  ADS  Google Scholar 

  48. K To, Phys. Rev. E71, 060301(R) (2005)

  49. I Zuriguel, L A Pugnaloni, A Garcimartín and D Maza, Phys. Rev. E68, 030301(R) (2003)

  50. I Zuriguel et al, Phys. Rev. E71, 051303 (2005)

  51. M Hou et al, Phys. Rev. Lett. 91, 204301 (2003)

  52. E Clément et al, Traffic and granular flow’ 99 edited by D Helbing, H J Herrmann, M Schreckenberg and D E Wolf (Springer, Berlin, 2000)

    Google Scholar 

  53. J Zhong, M Hou, Q Shi and K Lu, J. Phys.: Condens. Matter 18, 2789 (2006)

    Article  ADS  Google Scholar 

  54. G H Ristow and H J Herrmann, Phys. Rev. E50, R5 (1994)

    ADS  Google Scholar 

  55. S S Manna and H J Herrmann, Eur. Phys. J. E1, 341 (2000)

    Google Scholar 

  56. P Bak, C Tang and K Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  57. L E Silbert et al, Phys. Rev. E64, 051302 (2001)

  58. D Hirschfeld and D C Rapaport, Eur. Phys. J. E4, 193 (2001)

    Google Scholar 

  59. I Zuriguel, Ph.D. Thesis (Universidad de Navarra, 2005) (in Spanish)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gabriel Pérez.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pérez, G. Numerical simulations in granular matter: The discharge of a 2D silo. Pramana - J Phys 70, 989–1007 (2008). https://doi.org/10.1007/s12043-008-0104-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12043-008-0104-2

Keywords

PACS Nos

Navigation