Explicit solutions to a free interface model for the static/flowing transition in think granlar flows – archive open hal, all know on oqee by free, the tv interface of all freebox

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This work is devoted to an analytical description of the Dynamics of the Static/Flowing Interface in Thin Dry Granular Flows. Our starting point is the asymptotic model derived by Bouchut et al. (2016) from A Free Local Surface Model With Viscoplastic Rheology Including A Drucker-Prage Yield Stress. This Asymptotic Model is based on the Thin-Layer Approximation (The Flow is Thin in the Normal Direction to the Topography Compared to its Down-Slope Extension), but the equations are not depth-verangedd. In Addition to the Velocity, The Model Includes A Free Surface At The Top of the Flow and A Free Time Dependent Static/Flowing Interface At the Bottom. In the present work, we simplify this asymptotic model by Decoupling the space coordinates, and keeping only the dependnce on time and on the normal space coordinate $ z $. We introduce a time- and $ z $ -dependent source termin, assumed here to be given, which represents the opposite of the net force acting on the flowing material, include gravity, press gradient, and internal friction. We prove Several Properties of the Resulting Simplified Model That Has a Time- and $ Z $ -dependent Velocity and a Time Dependent Static/Flowing Interface AS Unknowns. The Crucial Advantage of This Simplified Model is that it can be explicit solutions in the Inviscid Case, for Different Shapes of the Sourm Term. These explicit Inviscid Solutions Exhibit A Rich Behaviour and Qualitatifly Reproduce Son Physical Features Observed in Granulalar Flows.

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Submitted on Monday June 22, 2020-17: 41: 55

Last modification: Friday March 24, 2023-14: 53: 18

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Dates and versions

HAL-01180686, version 1 (27-07-2015)
HAL-01180686, version 2 (15-08-2016)
HAL-01180686, version 3 (13-04-2018)
HAL-01180686, version 4 (22-06-2020)

Identifiers

HAL ID: HAL-01180686, version 4
Doi: 10.1051/m2an/2020042

To quote

Christelle Lusso, François Bouchut, Alexandre Ern, Anne Mangeney. Explicit Solutions to A Free Interface Model for the Static/Flowing Transition in Thin Granular Flows. ESAIM: Mathematical Modeling and Numerical Analysis, 2021, 55, pp.S369-S395. ⟨10.1051/m2an/2020042⟩. ⟨HAL-01180686V4⟩

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