The present paper shows for the first time in the literature a complete 2D simulation of the ozone production in a DC positive multi-tip to plane corona discharge reactor crossed by a dry air flow at atmospheric pressure. The simulation is undertaken until 1 ms and involves tens of successive discharge and post-discharge phases. The air flow is stressed by several monofilament corona discharges generated by a maximum of four anodic tips distributed along the reactor. The nonstationary hydrodynamics model for reactive gas mixture is solved using the commercial FLUENT software. During each discharge phase, thermal and vibrational energies as well as densities of radical and metastable excited species are locally injected as source terms in the gas medium surrounding each tip. The chosen chemical model involves 10 neutral species reacting following 24 reactions. The obtained results allow us to follow the cartography of the temperature and the ozone production inside the corona reactor as a function of the number of high voltage anodic tips.