A second-order non-local model for granular flows

We determine a constitutive equation for developed three-dimensional granular flows based on a series of discrete element method simulations. In order to capture non-local phenomena, normal stress differences, and secondary flows, we extend a previously proposed granular temperature-sensitive rheological model by considering Rivlin-Ericksen tensors up to second order. Three model parameters are calibrated with the inertial number and a dimensionless granular temperature. We validate our model by running finite difference method simulations of inclined chute flows. The model successfully predicts the velocity and stress fields in this geometry, including secondary vortical flows that previous first-order models could not predict and slow creeping zones that local models miss. It simultaneously captures the non-trivial variation among diagonal components of the stress tensor throughout the domain.

Automated summary

We propose a constitutive equation for three-dimensional granular flows based on discrete element method simulations. By considering second-order Rivlin-Ericksen tensors, we extend an existing granular temperature-sensitive rheological model to capture non-local phenomena, normal stress differences, and secondary flows. Three model parameters are calibrated using the inertial number and a dimensionless granular temperature. The model is validated through finite difference method simulations of inclined chute flows, successfully predicting the velocity and stress fields, including previously unaccounted for secondary vortical flows and slow creeping zones.