A three-dimensional continuum model incorporating static and kinetic effects for granular flows with applications to collapse of a two-dimensional granular column

This work extends a one-dimensional continuum model for granular flows down inclined planes [C. H. Lee and C. J. Huang, “Kinetic-theory-based model of dense granular flows down inclined planes,” Phys. Fluids 24, 073303 (2012)] to solve three-dimensional problems involving both static and flow states. The new model decomposes the shear stress and pressure into enduring-contact and kinetic components. One novelty of the present model is the determination of the enduring-contact component of pressure, which is a composition of a pressure depending only on the volume fraction and a pressure derived from the dilatancy law together with the equation of state from the kinetic theory. Another novelty of this study is a new numerical scheme that can avoid numerical instability caused by large volume fractions. To demonstrate its capability, the present model is applied to simulate the collapse of a granular column with various aspect ratios. The evolution of the column shape, the flow field, the final height, and the run-out predicted by the present model agree well with those provided by discrete element methods and experiments.