Exact solution for granular flows - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue International Journal for Numerical and Analytical Methods in Geomechanics Année : 2012

Exact solution for granular flows

Résumé

In this paper we present the exact solution of the Riemann problem for the non-linear one-dimensional socalled shallow-water or Saint-Venant equations with friction proposed by SAVAGE and HUTTER to describe debris avalanches. This model is based on the depth-averaged thin layer approximation of granular flows over sloping beds and takes into account a Coulomb type friction law with a constant friction coefficient. A particular configuration of the Riemann problem corresponds to a dam of infinite length in one direction from which granular material is released from rest at a given time over an inclined rigid or erodible bed. We solve analytically and numerically the depth-averaged long-wave equations derived in a topographylinked coordinate system for all the possible Riemann problems. The detailed mathematical proof of the derivation of the analytical solutions and the analysis of their structure and properties is intended first of all for geophysicists, mathematicians and physicists because of the possible extension of this study to more complex problems (geometries, friction laws,. . . ). The numerical solution of a first-order finitevolume method based on a Godunov-type scheme is compared with the proposed exact Riemann problem solution. This solution is used to solve the dam-break problem and analyze the influence of the thickness of the erodible bed on the speed of the granular front. Comparison with existing experimental results shows that, for an erodible bed, the equations lack fundamental physical significance to reproduce the observed dynamics of erosive granular flows
Fichier principal
Vignette du fichier
FM_exact.pdf (3.24 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00776614 , version 1 (27-02-2020)

Identifiants

Citer

Gloria Faccanoni, Anne Mangeney. Exact solution for granular flows. International Journal for Numerical and Analytical Methods in Geomechanics, 2012, 37 (10), pp.1408-1433. ⟨10.1002/nag.2124⟩. ⟨hal-00776614⟩
343 Consultations
171 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More