The constitutive laws of dense granular flow are investigated. Simulations of a drum, with periodic boundary conditions, rotating at varying speeds are performed. From the resulting data, kinematic and kinetic fields are extracted and used to investigate the validity of constitutive relations proposed in the literature. Two key constitutive assumptions are (a) isotropy and (b) incompressibility. The rotating drum system is found to be largely isotropic for high rotational speeds. For low rotational speeds, anisotropy is observed in the bottom part of the system, where the particles are flowing upwards. A small degree of compressibility is observed in the downward-flowing layer. The friction coefficient for the granular constitutive relations is also investigated. An empirically-derived friction law has a better fit to the data when compared to other friction laws proposed in the literature. Lastly, two scaling laws are investigated: the scaling between the scaled flow-rate (flux) and the thickness of the downward- flowing layer and the scaling between the dynamic angle of repose of the bed and the flux through the downward- flowing layer. The thickness-flux scaling is measured by interpolating the flux over a number of slices through the flowing layer, this is done in a number of different ways. The size of the measured section through the flowing layer is varied. The orientation of the slices is also varied. Also investigated is whether the total velocity or the tangential velocity produce the same scaling. The size of the section of the flowing layer significantly changes the scaling, this shows that the scaling is not constant throughout the flowing layer. The dynamic angle of repose is determined using two methods, one which is determined unambiguously as the repose angle of the ellipse fitted to the equilibrium surface and the other which is the changing angle of the tangent to the equilibrium surface or free surface. The first repose angle is found to be highly dependent on the flux even in the limit of infinite drum length, which is modelled using axial periodic boundary conditions. The second definition results in two sets of repose angles with complex behaviour that may be due to inertial effects. An instability in the system is observed, this is conjectured to be due to a frictional threshold that is breached as the rotational speed of the drum increases. Algorithms for calculating field variables and features of the charge are presented
