Three test cases for positive streamers in dry air at 1 bar and 300 K. Discharges are simulated between planar electrodes in a square domain with a radius and height of 1.25 cm. A background electric field of 15 kV/cm is present, which is well below the breakdown value. To locally enhance the electric field to values above the breakdown threshold, a Gaussian distribution of positive ions is placed below the anode. First test case: constant initial background density of electrons and Ions of 10¹³ m⁻³, no photoionization; second test case: constant initial background density of electrons and ions of 10⁹ m⁻³, no photoionization; third test case: constant initial background density of electrons and ions of 10⁹ m⁻³, photoionization included.