Artículo
A bed pressure correction of the friction term for depth-averaged granular flow models
Autor/es | Bouchut, François
Delgado Sánchez, Juan Manuel Fernández Nieto, Enrique Domingo Mangeney, Anne Narbona Reina, Gladys |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2022 |
Fecha de depósito | 2022-03-21 |
Publicado en |
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Resumen | Depth-averaged models, such as the Savage-Hutter model with Coulomb or Pouliquen fric tion laws, do not in some cases preserve the physical threshold of motion. In particular, the
simulated granular mass can start to flow ... Depth-averaged models, such as the Savage-Hutter model with Coulomb or Pouliquen fric tion laws, do not in some cases preserve the physical threshold of motion. In particular, the simulated granular mass can start to flow (or stay at rest) even if the slope angle of its free surface is lower (or higher) than the repose angle of the granular material involved. The problem is related to the hydrostatic pressure assumption, associated with the direction of integration, which is orthogonal to a reference plane or a reference bottom. We propose here an initial method to correct this misleading behavior. Firstly, we define a correction of the friction term that accounts for the Jacobian of a change of coordinates, making it possible to reproduce the physical threshold of motion and thus the solutions at rest. Sec ondly, we observe that the 3D model presented in [F. Bouchut, I. Ionescu, and A. Mangeney. An analytic approach for the evolution of the static-flowing interface in viscoplastic granular flows. Commun, Math. Sci., 14(8):2101–2126, 2016] verifies the physical thresholds of mo tion because it is based on a second order correction of the pressure valid for slow granu lar flows. The correction proposed here ensures that the model preserves, up to the second order, the physical threshold of motion defined by the repose angle of the material. Sev eral numerical tests are presented to illustrate certain problems related to classical depth averaged models and the remedial effect of the proposed correction, in particular through comparisons with experimental data. We finally show that this correction is not exact far from the starting and stopping phases of the granular avalanche and should be improved by adding other second order terms in the pressure approximation |
Agencias financiadoras | Ministerio de Ciencia, Innovación y Universidades (MICINN). España European Research Council (ERC) |
Identificador del proyecto | RTI2018- 096064-B-C22
ERC-CG-2013-PE10-617472 SLIDEQUAKES |
Cita | Bouchut, F., Delgado Sánchez, J.M., Fernández Nieto, E.D., Mangeney, A. y Narbona Reina, G. (2022). A bed pressure correction of the friction term for depth-averaged granular flow models. Applied Mathematical Modelling, 106 (June 2022), 627-658. |
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