Zonal flows are known to be a key player in the regulation of drift-wave turbulence and have been observed in a wide variety of plasma devices. Current attempts to describe the formation and dynamics of zonal flows and drift-waves in a simple magnetized column via numerical simulation of the Hasegawa–Wakatani model are described here. The simulations are shown to exhibit the formation of a zonal flow whose profile is well-predicted by analytic theory and in qualitative agreement with experimental observations. However, the magnitude of the zonal flow and fluctuation levels appear to be significantly overestimated by the simulation. Details of the numerical model and sensitivity to initial conditions are also described.