  We study the time-dependent flow behavior of gravity-driven free surface
granular flows using the discrete element method and continuum modeling.
Discrete element method (DEM) simulations of slightly polydisperse disks
flowing over a periodic chute with a bumpy base are performed. A simple
numerical solution based on a continuum approach with the inertial number based
$\mu-I$ rheology has been proposed to predict the flow dynamics. The results of
the continuum model are compared with the DEM simulation results for a wide
range of chute inclinations. Solutions for the constitutive model described by
the popular JFP model as well as the recently proposed modified rheological
model using a non-monotonic variation of $\mu-I$ are obtained. Our results
demonstrate that the popular JFP model reliably predicts the flow at low to
moderate inclination angles (i.e. for $I \lesssim 0.5$). However, it fails to
predict the flow properties at high inclinations. The modified rheological
model, on the other hand, is very well able to predict the time-averaged flow
properties for all the inclination angles considered in this study. Accounting
for the presence of the slip velocity, layer dilation, and stress anisotropy
are found to be crucial for accurate predictions of transient flows at high
inertial numbers (i.e. for $I > 1$).
