A dielectric barrier discharge actuator to control airflow along a flat dielectric plate has been numerically investigated in this paper. In order to avoid large computing times, streamers, Trichel pulses and the ionic reactions involving photons and electrons are neglected. The numerical model assumes two types of generic ions, one positive and one negative, whose drift in the electric field produces the electrohydrodynamic flow. This study provides detailed insights into the physical mechanisms of DBD that include the electric field, space charge transport, surface charge accumulation and air flow motion. The results show the V-I characteristics, velocity profiles and drag force estimates. In addition, the effects of the voltage level, frequency and inlet air velocity on the actuator performance are presented and interpreted. The simulation results show a good agreement with theoretical expectations and experimental data available in literature.