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

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.

[1]  Algirdas Maknickas,et al.  Parallel discrete element simulation of poly-dispersed granular material , 2010, Adv. Eng. Softw..

[2]  Sergio Nesmachnow,et al.  Granular physics in low-gravity environments using discrete element method , 2012 .

[3]  Dimitri Gidaspow,et al.  Investigation of mixing/segregation of mixture particles in gas-solid fluidized beds , 2007 .

[4]  Aibing Yu,et al.  A theoretical analysis of the force models in discrete element method , 2006 .

[5]  Kazuya Yoshida,et al.  Touchdown of the Hayabusa Spacecraft at the Muses Sea on Itokawa , 2006, Science.

[6]  J. van de Velde,et al.  The flow of granular solids through orifices , 1961 .

[7]  G. Grest,et al.  Granular flow down an inclined plane: Bagnold scaling and rheology. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  J. Stadel.  Cosmological N-body simulations and their analysis , 2001 .

[9]  Luis A. Godoy,et al.  A viscoplastic approach to model the flow of granular solids , 2000 .

[10]  Derek C. Richardson,et al.  Numerical simulations of asteroids modelled as gravitational aggregates with cohesion , 2009 .

[11]  T. Pöschel,et al.  Molecular dynamics simulation of size segregation in three dimensions , 1996 .

[12]  P. Michel,et al.  Numerical simulations of granular dynamics: I. Hard-sphere discrete element method and tests , 2011, 1306.2528.

[13]  Pawel Kosinski,et al.  Extension of the hard-sphere particle-wall collision model to account for particle deposition. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  J. H. Shaxby,et al.  On the properties of powders. The variation of pressure with depth in columns of powders , 1923 .

[15]  K. Holsapple.  Equilibrium figures of spinning bodies with self-gravity , 2004 .

[16]  D. C. Hong,et al.  Molecular dynamics simulations of hard sphere granular particles , 1992 .

[17]  Daniel Heisselmann,et al.  The Flow Of Granular Matter Under Reduced‐Gravity Conditions , 2009 .

[18]  George Lake,et al.  Direct Large-Scale N-Body Simulations of Planetesimal Dynamics , 2000 .

[19]  D. Scheeres,et al.  SIMULATING ASTEROID RUBBLE PILES WITH A SELF-GRAVITATING SOFT-SPHERE DISTINCT ELEMENT METHOD MODEL , 2011 .

[20]  A. Yu,et al.  Rolling friction in the dynamic simulation of sandpile formation , 1999 .

[21]  S. Tremaine,et al.  Symplectic integrators for solar system dynamics , 1992 .

[22]  K. M. Khan,et al.  Comment on “Rolling friction in the dynamic simulation of sandpile formation” ☆ , 2005 .

[23]  Hiroki Senshu,et al.  Numerical simulation of impact cratering on granular material , 2006 .

[24]  Joseph A. Burns,et al.  Approximate Equilibrium Shapes for Spinning, Gravitating Rubble Asteroids , 2007 .

[25]  Yutaka Tsuji,et al.  Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe , 1992 .

[26]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[27]  K. Holsapple,et al.  Tidal disruptions: II. A continuum theory for solid bodies with strength, with applications to the Solar System , 2008 .

[28]  T. Quinn,et al.  A SYMPLECTIC INTEGRATOR FOR HILL'S EQUATIONS , 2009, 0908.2269.

[29]  Guy T. Houlsby,et al.  The flow of granular materials—I: Discharge rates from hoppers , 1982 .

[30]  Anita Mehta,et al.  Granular Physics: Index , 2007 .

[31]  F. Bertrand,et al.  DEM-based models for the mixing of granular materials , 2005 .

[32]  Paul W. Cleary,et al.  Predicting charge motion, power draw, segregation and wear in ball mills using discrete element methods , 1998 .

[33]  David P. O'Brien,et al.  The global effects of impact-induced seismic activity on fractured asteroid surface morphology , 2005 .

[34]  Paul W. Cleary,et al.  DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge , 2002 .

[35]  H. Janssen.  Versuche uber Getreidedruck in Silozellen , 1895 .