Surface flows of granular materials: a short introduction to some recent models

Aradian, Ashod; Raphaël, Élie; Gennes, Pierre‐Gilles de

doi:10.1016/s1631-0705(02)01304-x

Cited by 48 publications

(50 citation statements)

References 22 publications

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“…A dry, low cohesive, granular system can be considered as a system with two layers; the standing layer, that forms the slope or the heap of the system, and the rolling layer, that is a thin layer that flows on the surface of the slope [1]. This behaviour can be modelled by means of a set of partial differential equations [8] that describe the evolution of these layers' thickness.…”

Section: Granular Systems Modellingmentioning

confidence: 99%

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Interactive Terrain Simulation and Force Distribution Models in Sand Piles

Pla‐Castells¹,

García-Fernández

Martı́nez

2006

Lecture Notes in Computer Science

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Abstract. This paper presents an application of Cellular Automata in the field of dry Granular Systems modelling. While the study of granular systems is not a recent field, no efficient models exist, from a computational point of view, in classical methodologies. Some previous works showed that the use of Cellular Automata is suitable for the development of models that can be used in real time applications. This paper extends the existing Cellular Automata models in order to make them interactive. A model for the reaction to external forces and a pressure distribution model are presented and analyzed, with numerical examples and simulations.

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Section: Granular Systems Modellingmentioning

confidence: 99%

“…The traditional approach uses fluid models and particle system models for describing the flow of granular material and the formation of heaps [1]. However, granular systems show characteristics, such as the appearance of macroscopic patterns or avalanches, that cannot be properly modelled using this approach.…”

Section: Introductionmentioning

confidence: 99%

Interactive Terrain Simulation and Force Distribution Models in Sand Piles

Pla‐Castells¹,

García-Fernández

Martı́nez

2006

Lecture Notes in Computer Science

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“…The closure relation making it possible to derive an equation for the static/flowing interface will be discussed and compared with different previously proposed models ( [7], [8], [2], [13], [12]). In particular, the existence of an energy equation for the different systems will be investigated.…”

Section: Introductionmentioning

confidence: 99%

“…where γ is an empirical constant (see also [1], [2]). The model proposed by Boutreux, Raphaël and DeGennes (BRDG model, see [8]) differs in the form of the exchange term, where h is replaced by a thickness λ smaller than h,…”

Section: Introductionmentioning

confidence: 99%

On new erosion models of Savage–Hutter type for avalanches

Bouchut¹,

Fernández-Nieto²,

Mangeney³

et al. 2008

Acta Mech

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In this work we study the modeling of one-dimensional avalanche flows made of a moving layer over a static base, where the interface between the two can be time dependent. We propose a general model, obtained by looking for an approximate solution with constant velocity profile to the incompressible Euler equations. This model has an energy dissipation equation that is consistent with the depth integrated energy equation of the Euler system. It has physically relevant steady state solutions, and, for constant slope, it gives a particular exact solution to the incompressible hydrostatic Euler equations. Then, we propose a simplified model, for which the energy conservation holds only up to third-order terms. Its associated eigenvalues depend on the mass exchange velocity between the static and moving layers. We show that a simplification used in some previously proposed models gives a nonconsistent energy equation. Our models do not use, nor provide, any equation for the moving interface, thus other arguments have to be used in order to close the system. With special assumptions, and in particular small velocity, we can nevertheless obtain an equation for the evolution of the interface. Furthermore, the unknown parameters of the model proposed by Bouchaud, Cates, Ravi and Edwards (BCRE model [7]) can be derived. For the quasistationary case we compare and discuss the equation for the moving interface with Khakhar's model [13].

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“…The final angle varies around a value a bit below the angle of repose of 28°(which we measured using the funnel method), in contrast to the much smaller final crater angle reported in experiments of solid ball impact and the collapse of a cylindrical cavity in granular media [83,120]. It has been shown from a phenomenological model (of the BCRE-type 4 ) that the final crater slope depends significantly on the initial condition [121,122]. Therefore, one plausible reason of our comparatively large final angle observations is that the transient crater angle never exceeds 50°, while the collapse of a cavity created by solid ball impact are typically at a higher impact energy which may well cause much larger transient angles.…”

Section: Crater Slopementioning

confidence: 53%

The impact of raindrops on sand

Jong¹

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Surface flows of granular materials: a short introduction to some recent models

Cited by 48 publications

References 22 publications

Interactive Terrain Simulation and Force Distribution Models in Sand Piles

Interactive Terrain Simulation and Force Distribution Models in Sand Piles

On new erosion models of Savage–Hutter type for avalanches

The impact of raindrops on sand

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