Eur. Phys. J. B 68, 619-627 (2009)
https://doi.org/10.1140/epjb/e2009-00123-6

Euler-like modelling of dense granular flows: application to a rotating drum

¹ CEA, IRAMIS, SPCSI, Grp. Complex Systems & Fracture, 91191 Gif-sur-Yvette, France
² Laboratoire de Physique Théorique, CNRS UMR 5152, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France
³ CEA, IRAMIS, SPEC, CNRS URA 2464, Groupe Instabilités & Turbulence, 91191 Gif-sur-Yvette, France
⁴ Equipe TMI, LaMCoS, CNRS UMR 5259, INSA Lyon, 18-20 rue des sciences, 69621 Villeurbanne, France

Corresponding author: ^a francois.daviaud@cea.fr

Received: 28 November 2008
Revised: 23 February 2009
Published online: 8 April 2009

Abstract

General conservation equations are derived for 2D dense granular flows from the Euler equation within the Boussinesq approximation. In steady flows, the 2D fields of granular temperature, vorticity and stream function are shown to be encoded in two scalar functions only. We checked such prediction on steady surface flows in a rotating drum simulated through the Non-Smooth Contact Dynamics method even though granular flows are dissipative and therefore not necessarily compatible with Euler equation. Finally, we briefly discuss some possible ways to predict theoretically these two functions using statistical mechanics.