Discrete Element and Continuum Modeling of Secondary Flows in Dense Granular Materials

We investigate secondary flows in the flow of dense granular materials across several geometries such as flows through non-axisymmetric channels. Using discrete element method simulations, we demonstrate the existence of weak secondary vortical flows in a direction perpendicular to the primary flow in such geometries. We explain the existence of these secondary flows based on a second-order rheological model that incorporates viscometric functions such as the normal stress differences. We implement the frame-invariant rheological model in an incompressible continuum flow solver and demonstrate good agreement between the predictions of velocity and stress fields by the continuum solver and the corresponding coarse-grained fields obtained from simulations using the discrete element method.