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Simulating streamer discharges in 3D can computationally be very expensive,which is why 2D Cartesian simulations are sometimes used instead, especiallywhen dealing with complex geometries. Although 2D Cartesian simulations canonly be used to obtain qualitative results, it is nevertheless interesting tounderstand how they differ from their 3D or axisymmetric counterparts. Wetherefore compare 2D Cartesian and axisymmetric simulations of positivestreamers in air, using a drift-diffusion-reaction fluid model with the localfield approximation. With the same electrode length and width, inceptionvoltages are found to be about a factor two higher in the 2D Cartesian case.When compared at the same applied voltage, the 2D Cartesian streamers are up tofour times thinner and slower, their maximal electric field is about 30% lowerand their degree of ionization is about 65% lower, with the largest differencesoccurring at the start of the discharge. When we compare at a similar ratio ofapplied voltage over inception voltage, velocities become rather similar, andso do the streamer radii at later propagation times. However, the maximalelectric field in the 2D Cartesian case is then about 20-30% lower, and thedegree of ionization is about 40-50% lower. Finally, we show that streamerbranching cannot qualitatively be modeled in a 2D Cartesian geometry.

A model comparison of 2D Cartesian and 2D axisymmetric models for positive streamer discharges in air