Spatial uniformity is important in most applications of dielectric barrier discharges operating at atmospheric pressure. However, such uniformity is not easily achieved. Under many conditions, a filamentary structure usually develops. In this paper, we employ a two-dimensional self-consistent fluid model to explore the influence of several factors on the evolution of spatial structure of dielectric barrier discharges. In particular, we contrast the behaviour of discharges in pure helium and He-N2 gas mixture, which represent the reduction in breakdown voltage of gas during the evolvement of uniform glow discharge plasma. The transformation from filamentary to uniform mode of discharge plasma is analyzed by the phenomenon of coalescence of filaments and we investigate the effect of several external discharge parameters, such as driving frequency and effect of overvoltage, and the dielectric constant of the barrier material for the uniform and filamentary discharge plasmas. This simulation study is useful to describe the spatio-temporal profiles of electrons density in different phases of the filamentary, uniform Townsend and glow discharge regimes under various constraints.