The kinetically-constrained Kob-Andersen model has proven to be efficient in describing granular matter close to jamming. The model allows to calculate numerically the current of particles propagating through a lattice, the particle density distribution and even evaluate spatial correlations between the particles and the effect of these correlations on measurable parameters such as current. This simple model also allows to analytically predict the probability of the system to be in a jammed state, or to detect particles that will never be able to move.

We simulate the movement of granular matter through an opening subjected to a constant gravitational field. We study the behavior as a function of opening size, initial conditions, system size, particle density and the acceleration of gravity. To that end, we constructed a computationally efficient Monte-Carlo simulation, which implements a rejection-free algorithm. We also study the model without any obstacles with periodic boundary conditions (the bulk model). We have built a mean field theory to this model and we see from the simulations that correlations break mean field behavior and give rise to the non-monotonic behavior of current as a function of the driving field.