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An implementation of the soft-sphere discrete element method in a high-performance parallel gravity tree-code

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Abstract

We present our implementation of the soft-sphere discrete element method (SSDEM) in the parallel gravitational N-body code pkdgrav, a well-tested simulation package that has been used to provide many successful results in the field of planetary science. The implementation of SSDEM allows for the modeling of the different contact forces between particles in granular material, such as various kinds of friction, including rolling and twisting friction, and the normal and tangential deformation of colliding particles. Such modeling is particularly important in regimes for which collisions cannot be treated as instantaneous or as occurring at a single point of contact on the particles’ surfaces, as is done in the hard-sphere discrete element method already implemented in the code. We check the validity of our soft-sphere model by reproducing successfully the dynamics of flows in a cylindrical hopper. Other tests will be performed in the future for different dynamical contexts, including the presence of external and self-gravity, as our code also includes interparticle gravitational force computations. This will then allow us to apply our tool with confidence to planetary science studies, such as those aimed at understanding the dynamics of regolith on solid celestial body surfaces, or at designing efficient sampling tools for sample-return space missions.

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References

  1. Yano H. et al.: Touchdown of the Hayabusa Spacecraft at the Muses Sea on Itokawa. Science 312, 1350–1353 (2006)

    Article  ADS  Google Scholar 

  2. Richardson J.E., Melosh H.J., Greenberg R.J., O’Brien D.P.: The global effects of impact-induced seismic activity on fractured asteroid surface morphology. Icarus 179, 325–349 (2005)

    Article  ADS  Google Scholar 

  3. Richardson D.C., Walsh K.J., Murdoch N., Michel P.: Numerical simulations of granular dynamics: I. Hard-sphere discrete element method and tests. Icarus 212, 427–437 (2011)

    Article  ADS  Google Scholar 

  4. Mehta A.J.: Granular Physics. Cambridge University Press, New York (2007)

    Book  MATH  Google Scholar 

  5. Cleary P.W., Sawley M.L.: DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Appl. Math. Model. 26, 89–111 (2002)

    Article  MATH  Google Scholar 

  6. Kacianauskas R., Maknickas A., Kaceniauskas A., Markauskas D., Balevicius R.: Parallel discrete element simulation of poly-dispersed granular material. Adv. Eng. Softw. 41, 52–63 (2010)

    Article  MATH  Google Scholar 

  7. Elaskar S.A., Godoy L.A., Gray D.D., Stiles J.M.: A viscoplastic approach to model the flow of granular solids. Int. J. Solids Struct. 37, 2185–2214 (2000)

    Article  MATH  Google Scholar 

  8. Holsapple K.A.: Equilibrium figures of spinning bodies with self-gravity. Icarus 172, 272–303 (2004)

    Article  ADS  Google Scholar 

  9. Holsapple K.A., Michel P.: Tidal disruptions. II. A continuum theory for solid bodies with strength, with applications to the solar system. Icarus 193, 283–301 (2008)

    Article  ADS  Google Scholar 

  10. Sharma I., Jenkins J.T., Burns J.A.: Dynamical passage to approximate equilibrium shapes for spinning, gravitating rubble asteroids. Icarus 200, 304–322 (2009)

    Article  ADS  Google Scholar 

  11. Wada K., Senshu H., Matsui T.: Numerical simulation of impact cratering on granular material. Icarus 180, 528–545 (2006)

    Article  ADS  Google Scholar 

  12. Hong D.C., McLennan J.A.: Molecular dynamics simulations of hard sphere granular particles. Phys. A 187, 159–171 (1992)

    Article  Google Scholar 

  13. Huilin L., Yunhua Z., Ding J., Gidaspow D., Wei L.: Investigation of mixing/segregation of mixture particles in gas-solid fluidized beds. Chem. Eng. Sci. 62, 301–317 (2007)

    Article  Google Scholar 

  14. Kosinski P., Hoffmann A.C.: Extension of the hard-sphere particle-wall collision model to account for particle deposition. Phys. Rev. E 79, 061302 (2009)

    Article  ADS  Google Scholar 

  15. Tsuji Y., Tanaka T., Ishida T.: Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol. 71, 239–250 (1992)

    Article  Google Scholar 

  16. Sànchez P., Scheeres D.J.: Simulating asteroid rubble piles with a self-gravitating soft-sphere distinct element method model. ApJ 727, 120 (2011)

    Article  ADS  Google Scholar 

  17. Tancredi, G., Maciel, A., Heredia, L., Richeri, P., Nesmachnow, S.: Granular physics in low-gravity environments using DEM. MNRAS 420, 3368–3380 (2012)

    Google Scholar 

  18. Gallas J.A.C., Hermann H.J., Pöschel T., Sokolowski S.: Molecular dynamics simulation of size segregation in three dimensions. J. Stat. Phys. 82, 443–450 (1996)

    Article  ADS  Google Scholar 

  19. Silbert L.E., Ertaş D., Grest G.S., Halsey T.C., Levine D., Plimpton S.J.: Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64, 051302 (2001)

    Article  ADS  Google Scholar 

  20. Stadel J.: Cosmological N-body simulations and their analysis, pp. 126. University of Washington, Washington, DC (2001)

    Google Scholar 

  21. Richardson D.C., Quinn T., Stadel J., Lake G.: Direct large-scale N-body simulations of planetesimal dynamics. Icarus 143, 45–59 (2000)

    Article  ADS  Google Scholar 

  22. Richardson D.C., Michel P., Walsh K.J., Flynn K.W.: Numerical simulations of asteroids modelled as gravitational aggregates with cohesion. Planet. Space Sci. 57, 183–192 (2009)

    Article  ADS  Google Scholar 

  23. Cundall P.A., Strack O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29, 47–65 (1979)

    Article  Google Scholar 

  24. Saha P., Tremaine S.: Symplectic integrators for solar system dynamics. Astron. J. 104, 1633–1640 (1992)

    Article  ADS  Google Scholar 

  25. Quinn T., Perrine R.P., Richardson D.C., Barnes R.: A Symplectic integrator for Hill’s equations. ApJ 139, 803–807 (2010)

    ADS  Google Scholar 

  26. Cleary P.W.: Predicting charge motion, power draw, segregation and wear in ball mills using discrete element methods. Min. Eng. 11, 1061–1080 (1998)

    Article  Google Scholar 

  27. Zhou Y.C., Wright B.D., Yang R.Y., Xu B.H., Yu A.B.: Rolling friction in the dynamic simulation of sandpile formation. Phys. A 269, 536–553 (1999)

    Article  Google Scholar 

  28. Kahn K.M., Bushell G.: Comment on rolling friction in the dynamic simulation of sandpile formation. Phys. A 352, 522–524 (2005)

    Article  Google Scholar 

  29. Zhu H.P., Yu A.B.: A theoretical analysis of the force models in discrete element method. Powder Technol. 161, 122–129 (2006)

    Article  Google Scholar 

  30. Nedderman R.M., Tüzün U., Savage S.B., Houlsby G.T.: The flow of granular materials–I: discharge rates from Hoppers. Chem. Eng. Sci. 37, 1597–1609 (1982)

    Article  Google Scholar 

  31. Bertrand F., Leclaire L.-A., Levecque G.: DEM-based models for the mixing of granular materials. Chem. Eng. Sci. 60, 2517–2531 (2005)

    Article  Google Scholar 

  32. Beverloo W.A., Leniger H.A., van de Velde J.: The flow of granular solids through orifices. Chem. Eng. Sci. 15, 260–269 (1961)

    Article  Google Scholar 

  33. Janssen H.A.: Versuche über Getreidedruck in Silozellen. Ver. dt. Ing. 39, 1045–1049 (1895)

    Google Scholar 

  34. Shaxby J.H., Evans J.C.: The variation of pressure with depth in columns of powders. Trans. Faraday Soc. 19, 60–72 (1923)

    Article  Google Scholar 

  35. Rose H.E., Tanaka T.: Rate of discharge of granular materials from bins and hoppers. Engineer 208, 465–469 (1959)

    Google Scholar 

  36. Hofmeister, P., Blum, J., Heißelmann, D.: The flow of granular matter under reduced-gravity conditions. In: Nakagawa M., Luding S. (eds.) Powders and Grains 2009: Proceedings of the 6th International Conference on Micromechanics of Granular Media, Hrsg. AIP Conference Proceedings vol. 1145, pp. 71–74 (2009)

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Authors and Affiliations

  1. Department of Astronomy, University of Maryland, College Park, MD, 20742-2421, USA

    Stephen R. Schwartz & Derek C. Richardson

  2. Lagrange Laboratory, University of Nice Sophia Antipolis, CNRS, Côte d’Azur Observatory, Observatoire de la Côte d’Azur, B.P. 4229, 06304, Nice Cedex 4, France

    Stephen R. Schwartz & Patrick Michel

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  1. Stephen R. Schwartz
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  2. Derek C. Richardson
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Correspondence to Stephen R. Schwartz.

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Schwartz, S.R., Richardson, D.C. & Michel, P. An implementation of the soft-sphere discrete element method in a high-performance parallel gravity tree-code. Granular Matter 14, 363–380 (2012). https://doi.org/10.1007/s10035-012-0346-z

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