Skip to Main content Skip to Navigation
Journal articles

Exact solution for granular flows

Abstract : 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
Document type :
Journal articles
Complete list of metadata

Cited literature [48 references]  Display  Hide  Download

https://hal.inria.fr/hal-00776614
Contributor : Jacques Sainte-Marie <>
Submitted on : Thursday, February 27, 2020 - 11:30:33 AM
Last modification on : Wednesday, June 30, 2021 - 9:40:07 PM
Long-term archiving on: : Thursday, May 28, 2020 - 2:48:42 PM

File

FM_exact.pdf
Files produced by the author(s)

Identifiers

Citation

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

Share

Metrics

Record views

877

Files downloads

928