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A new kinetic scheme for Saint-Venant equations applied to debris avalanches

Abstract : Numerical modelling of debris avalanches is presented here. The model uses the long waves approximation, based on the small aspect ratio of debris avalanches, as in classical Saint-Venant models for shallow water. Depth-averaged equations using this approximation are derived in a reference frame linked to the topography. Debris avalanches are treated here as a dry granular flow with Coulomb-type behavior. The numerical finite volume method uses a kinetic scheme, based on the description of the microscopic behavior of the system, to define numerical fluxes at the interfaces of a finite element mesh. The main advantage of this method is to preserve the height positivity. The originality of the present scheme stands in the introduction of a Dirac distribution of particles at the microscopic scale, in order to describe the stopping of a granular mass when the driving forces are under the Coulomb threshold. Comparisons with analytical solutions for dam-break problems show the efficiency of the method to deal with significant discontinuities. The ability of the model to describe debris avalanche behavior is illustrated here by schematic 1D numerical simulations of an avalanche over simplified topography. Coulomb-type behavior with constant and variable friction angle are compared in the framework of this simple example. Numerical tests show that such approach does not only provide insights into the flowing and stopping stage of the granular mass but it also allows us to observe interesting behaviors, such as the existence of a fluidized zone behind a stopped granular mass in specific situations, suggesting the presence of horizontal surfaces in the deposited mass.
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https://hal.inria.fr/inria-00071939
Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 7:19:00 PM
Last modification on : Tuesday, November 17, 2020 - 10:26:08 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:45:22 PM

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  • HAL Id : inria-00071939, version 1

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A. Mangeney-Castelnau, J.P. Vilotte, Marie-Odile Bristeau, François Bouchut, Benoît Perthame, et al.. A new kinetic scheme for Saint-Venant equations applied to debris avalanches. [Research Report] RR-4646, INRIA. 2002. ⟨inria-00071939⟩

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