A number of numerical hopper discharge experiments were conducted using a novel simulation technique in which the individual circular disc particles are allowed to fill a two-dimensional hopper under gravity and are subsequently discharged through a central slot orifice. The novel aspect of the present technique is the incorporation of a continuous potential interaction for frictional granular flows which ensures the stability of contact mechanical force algorithms over much larger time steps than were hitherto possible. This is achieved by allowing softer interactions which vary on the same scale as the nominal particle size rather than the micro-contact scale used in the majority of previous literature. The resulting technique allows the filling and discharge events to be simulated over a sufficiently long time scale. The continuous potential confers on the particles an "excluded volume" which prevents excessive overlap. In addition, the effects of frictional forces are introduced via a tangential displacement vs force model similar to that developed by Mindlin for contacts of perfectly elastic spheres, but scaled to the normal potential interaction. Transition from fluid-like to granular flow is simulated by increasing the friction coefficient from zero. During both the filling and discharge stages of the simulation, the radial and tangential components of particle velocities are damped by a force proportional to the relative particle velocities. The effects of material head in the hopper, the outlet size and the hopper half-angle were investigated to predict material discharge rates as well as the wall stress profiles during both filling and discharge. The effects of the ratio of the interparticle and wall friction coefficients on the prevailing flow and stress fields were also investigated in both "mass-flow" and "funnel-flow" hoppers. Encouraging agreement was found between the simulation and experimental flow behaviour.