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Numerical Modeling of Two-Phase Gravitational Granular Flows with Bottom Topography

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • M. Pelanti

    (École Normale Supérieure, Département de Mathématiques et Applications)

  • F. Bouchut

    (École Normale Supérieure, Département de Mathématiques et Applications)

  • A. Mangeney

    (IPGP, Département de modélisation physique et numérique
    Institut de Physique du Globe de Paris, Équipe de Sismologie)

  • J. -P. Vilotte

    (Institut de Physique du Globe de Paris, Équipe de Sismologie)

Abstract

We study a depth-averaged model of gravity-driven mixtures of solid grains and fluid moving over variable basal surface. The particular application we are interested in is the numerical description of geophysical flows such as avalanches and debris flows, which typically contain both solid material and interstitial fluid. The depth-averaged mass and momentum equations for the solid and fluid components form a nonconservative system, where nonconservative terms involving the derivatives of the unknowns couple together the sets of equations of the two phases. The system can be shown to be hyperbolic at least when the difference of velocities of the two constituents is sufficiently small. We numerically solve the model equations in one dimension by a finite volume scheme based on a Roe-type Riemann solver. Well-balancing of topography source terms is obtained via a technique that includes these contributions into the wave structure of the Riemann solution.

Suggested Citation

  • M. Pelanti & F. Bouchut & A. Mangeney & J. -P. Vilotte, 2008. "Numerical Modeling of Two-Phase Gravitational Granular Flows with Bottom Topography," Springer Books, in: Sylvie Benzoni-Gavage & Denis Serre (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 825-832, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75712-2_85
    DOI: 10.1007/978-3-540-75712-2_85
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