Plasma actuators generated by surface dielectric barrier discharge are developed for controlling flow in aeronautics applications. This research studies the simulation of cold plasma discharge at atmospheric pressure coupled with compressible fluid dynamics using COMSOL Multiphysics 5.4. Modeling of dielectric barrier discharge in air at high voltages is carried out in two dimensions. The development of electric field and space charge density are discussed in several cases to determine the discharge regime. Non-thermal plasma generates tangential ionic winds at the surface during corona discharge. The results are validated by the experimental results of the literature. The maximum electric wind velocity above the actuator grows linearly with the applied voltage, and simultaneously, the horizontal extension of the discharge grows with the applied voltage. The induced electrohydrodynamic force augments with the applied voltage amplitude, reaching saturation at higher voltages. Moreover, as the voltage rises, the discharge becomes filamentary, inducing a higher number of streamer pulses. Hence, the power consumption discharge increases abruptly as the voltage rises. In addition, the efficiency increases at higher voltage amplitudes and with the dielectric thickness. Our findings give a clear description of physical atmospheric plasma parameters in the surface discharge mechanism and the efficiency of the actuator plasma.