Volume diffusion modelling of a sheared granular gas

Continuum fluid dynamic models based on the Navier-Stokes equations have previously been used to simulate granular media undergoing fluid-like shearing. These models, however, typically fail to predict the flow behaviour in confined environments as non-equilibrium particle effects dominate near walls. We adapt an extended hydrodynamic model for granular flows, which uses a density-gradient dependent "volume diffusion'' term to correct the viscous stress tensor and heat flux, to simulate the shearing of a granular gas between two rough walls, and with corresponding boundary conditions. We use our volume diffusion model to predict channel flows for a range of mean volume fraction ϕ¯=0.01-0.4, and inter-particle coefficients of restitution e=0.8 and 0.9, and compare with Discrete Element Method (DEM) simulations and classical Navier-Stokes equations. Our model is capable of predicting non-uniform pressure, volume fraction and granular temperature, which become more significant for cases with mean volume fraction ϕ¯∼0.1, in which we typically observe non-uniform peak density variations, and large volume fraction gradients.