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This research work is devoted to 2D numerical modeling of particle transport (electrons and positive ions) in a high-pressure discharge (positive streamer). The electrode configuration is planar and the gas used is nitrogen. The fluid model was chosen (coupling of the first two moments of Boltzmann's equation: continuity equation and momentum transfer equation to Poisson's equation). The current density in the continuity equations was calculated using Scharfetter and Gummel's improved first-order numerical scheme (SG1). The scheme was established by Kulikovsky. The Poisson's equation is solved in 2D using the Biconjugate Gradient Stabilized (BICGSTAB) method. Electron density, ion density, axial electric field, net charge density, source term and external electric current along the propagation axis were obtained. The curves were plotted in one and two dimensions. The effect of initial conditions (effect of preionization background, effect of voltage and effect of radial dispersion) on the propagation of the electric discharge was also investigated.