Simulation of Gravity Flow of Granular Materials in Silos

  • Pierre A. Gremaud
  • John V. Matthews
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 11)


The problem of determining the steady state flow of granular materials in silos under the action of gravity is considered. In the case of a Mohr-Coulomb material, the stress equations correspond to a system of hyperbolic conservation laws with source terms and nonlinear boundary conditions. A higher order Discontinuous Galerkin method is proposed and implemented for the numerical resolution of those equations. The efficiency of the approach is illustrated by the computation of the stress fields induced in silos with sharp changes of the wall angle.


Granular Material Stress Equation Discontinuous Galerkin Method Granular Flow Radial Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cockburn, B., Lin, S.Y., Shu, C.W.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one dimensional systems. J. Comput. Phys. 84 (1989) 90–113MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Cockburn, B., Shu, C.W.: The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. Comput. Phys. 141 (1998) 199–224MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Gremaud, P.A., Matthews, J.V.: On the computation of hopper flows. In preparation.Google Scholar
  4. 4.
    Gremaud, P.A., Matthews, J.V., Shearer, M.: Similarity solutions for granular flows in hoppers. Proceedings of the SIAM/AMS Conference on Nonlinear PDEs, Dynamics and Continuum Physics, J. Bona, K. Saxton, R. Saxton, Eds., (1998), AMS Contemporary Mathematics Series, to be published.Google Scholar
  5. 5.
    Gremaud, P.A., Schaeffer, D., Shearer, M.: Numerical determination of flow corrective inserts for granular materials in conical hoppers. To be published in Int. J. Nonlinear Mech.Google Scholar
  6. 6.
    Jenike, A.: Gravity flows of bulk solids. Bulletin No. 108, vol. 52, Utah Eng. Expt. Station, University of Utah, Salt Lake City (1961)Google Scholar
  7. 7.
    Nedderman, R.M.: Static and kinematic of granular materials. Cambridge University Press (1992).CrossRefGoogle Scholar
  8. 8.
    Pitman, E.B.: The stability of granular flow in converging hoppers. SIAM J. Appl. Math. 48 (1988) 1033–1052MathSciNetzbMATHGoogle Scholar
  9. 9.
    Ravi Prakash, J., Kesava Rao, K.: Steady compressible flow of cohesionless granular materials through a wedge-shaped bunker. J. Fluid Mech. 225 (1991) 21–80MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Roe, P.L.: Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comp. Phys. 43 (1981) 357–372MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Royal, A.T.: Private communication. Jenike & Johanson, Inc. (1998).Google Scholar
  12. 12.
    Schaeffer, D.G.: Instability in the evolution equations describing incompressible granular flow. J. Diff. Eq. 66 (1987) 19–50.MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Shu, C.W., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comp. Phys. 77 (1988) 439–471.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Pierre A. Gremaud
    • 1
  • John V. Matthews
    • 1
  1. 1.Department of Mathematics and Center for Research in Scientific ComputationNorth Carolina State UniversityRaleighUSA

Personalised recommendations