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We present the results of two-dimensional computer simulations of streamer initiation and propagation in atmospheric pressure N2. The simulation algorithm makes use of flux-corrected transport techniques and was used as a tool to study the solutions of the transport equations under conditions suitable for streamers, for which realistic analytic solutions are not known. We present and discuss conclusions about streamer transport based on the results of these studies. Finally, we present a novel method of checking on the numerical accuracy with which the algorithm solves the transport equations.