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

TL;DR

This paper derives Euler-like conservation equations for dense granular flows, demonstrating that key flow fields depend on only two scalar functions, and validates this on rotating drum simulations.

Contribution

It introduces a novel Euler-like modeling framework for dense granular flows and verifies it through numerical simulations, linking flow fields to two scalar functions.

Findings

Flow fields depend on two scalar functions in steady conditions

Euler-like equations are applicable despite dissipative nature of granular flows

Validation performed on rotating drum simulations

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. This result is non trivial because 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.