Modeling flow arrest using a non-local rheology?

Abstract

Using an incompressible Navier-Stokes solver with a modified non-Newtonian viscosity, we implement the μ(I)-rheology and study the transient arrest for thick granular layers. In order to study the stopping height phenomenology Hstop, we implement the steady-state-only approximate version of the non-local model from [6, 7] and successfully incorporate this feature in the solver. We compare the velocity profiles for granular layer thicknesses close to Hstop given by the model with discrete simulations, and discuss the ability of the nonlocal model to describe the dynamics of the flow close to stopping height. We find that for flows with thickness close to Hstop, the velocity profiles given by the model do not reflect the behavior of discrete simulation: discrete velocity profiles remain self-similar when approaching Hstop, while the non-local rheology predicts a change of concavity near the bottom.