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A Numerical Study for Growing Sandpiles on Flat Tables with Walls

  • M. Falcone
  • S. Finzi Vita
Conference paper
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 202)

Abstract

We continue our study on the approximation of a system of partial differential equations recently proposed by Hadeler and Kuttler to model the dynamics of growing sandpiles on a flat bounded table. The novelty here is the introduction of (infinite) walls on the boundary of the domain and the corresponding modification of boundary conditions for the standing and for the rolling layers. An explicit finite difference scheme is introduced and new boundary conditions are analyzed. We show experiments in ID and 2D which characterize the steady-state solutions.

keywords

granular matter hyperbolic systems finite differences schemes 

References

  1. [1]
    G. Aronsson, L.C. Evans and Y. Wu. Fast/slow diffusion and growing sandpiles. J. Diff. Equations 131:304–335, 1996.MATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    P. Cannarsa and P. Cardaliaguet. Representation of equilibrium solutions to the table problem for growing sandpiles. JEMS 6:435–464, 2004.MATHMathSciNetGoogle Scholar
  3. [3]
    PG. de Gennes. Granular matter. In Summer School on Complex Systems, Varenna, Lecture Notes Società Italiana di Fisica 1996.Google Scholar
  4. [4]
    L.C. Evans, M. Feldman and R.F. Gariepy. Fast/slow diffusion and collapsing sandpiles. J. Diff. Equations 137:166–209, 1997.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    M. Falcone and S. Finzi Vita. A finite-difference approximation of a two-layer system for growing sandpiles, Dipartimento di Matematica, Preprint, May 2005 also available at http://cpde.iac.rm.cnr.it/preprint.php.Google Scholar
  6. [6]
    M. Falcone and S. Finzi Vita. Convergence of a finite-difference approximation of a two-layer system for growing sandpiles, in preparation.Google Scholar
  7. [7]
    S. Finzi Vita. Numerical simulation of growing sandpiles. In Control Systems: Theory, Numerics and Applications, CSTNA2005. e-published by SISSA, PoS (http://pos. sissa. it), 2005.Google Scholar
  8. [8]
    K.P Hadeler and C. Kuttler. Dynamical models for granular matter. Granular Matter 2:9–18, 1999.CrossRefGoogle Scholar
  9. [9]
    K.P. Hadeler, C. Kuttler and I. Gergert. Dirichlet and obstacle problems for granular matter. Preprint, University of Tübingen, 2002.Google Scholar
  10. [10]
    L. Prigozhin. Variational model of sandpile growth. Euro. J. Appl Math. 7:225–235,1996.MATHMathSciNetGoogle Scholar

Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • M. Falcone
    • 1
  • S. Finzi Vita
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma La SapienzaRomaItaly

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