Eur. Phys. J. E (2014) 37: 5
https://doi.org/10.1140/epje/i2014-14005-6

Regular Article

Continuum simulation of the discharge of the granular silo

A validation test for the μ(I) visco-plastic flow law

¹ School of Earth Sciences, University of Bristol, Queens Road, BR8 1RJ, Bristol, UK
² CNRS - Université Pierre et Marie Curie Paris 6, UMR 7190, Institut Jean Le Rond d’Alembert, F-75005, Paris, France
³ National Institute of Water and Atmospheric Research, PO Box 14-901, Kilbirnie, Wellington, New Zealand

^* e-mail: lydie.staron@upmc.fr
^** e-mail: staron@lmm.jussieu.fr

Received: 7 July 2013
Revised: 14 November 2013
Accepted: 17 January 2014
Published online: 30 January 2014

Abstract

Using a continuum Navier-Stokes solver with the μ(I) flow law implemented to model the viscous behavior, and the discrete Contact Dynamics algorithm, the discharge of granular silos is simulated in two dimensions from the early stages of the discharge until complete release of the material. In both cases, the Beverloo scaling is recovered. We first do not attempt a quantitative comparison, but focus on the qualitative behavior of velocity and pressure at different locations in the flow. A good agreement for the velocity is obtained in the regions of rapid flows, while areas of slow creep are not entirely captured by the continuum model. The pressure field shows a general good agreement, while bulk deformations are found to be similar in both approaches. The influence of the parameters of the μ(I) flow law is systematically investigated, showing the importance of the dependence on the inertial number I to achieve quantitative agreement between continuum and discrete discharge. However, potential problems involving the systems size, the configuration and “non-local” effects, are suggested. Yet the general ability of the continuum model to reproduce qualitatively the granular behavior is found to be very encouraging.