Most simulation findings regarding granular rollwaves are based on the analysis of steady uniform flows with an initial artificial perturbation. The difference in the scenario used in our study is that roll waves are generated by applying a zero-mean fluctuant flux inflow condition over the upstream boundary. Only the upstream section of the inclined chute is covered with a sheet of granules with no supplementary application of a boundary condition. Starting with the depth-averaged governing framework, the mu(Fr,h)-dynamic basal friction law, and the mu(I)-rheology-based second-order viscous terms, and adopting a second-order shock-capturing total variation diminishing-MacCormack scheme, we captured self-destabilized roll waves generated in an unsteady granular chute flow. In the simulated unsteady flow, three stages-wave spreading, wave forming and wave-collapseare identified and discussed. The simulation results are confirmed by observations in laboratory granular flow experiment and natural avalanches from other literatures. (C) 2020 Published by Elsevier B.V.