A thin, flexible plate electrode was adopted to generate both ionic wind and vibration in our previous study. The design contains a metal inductor placed next to the plate electrode so that it is attracted to vibrate by the induced electrostatic force. The resulting flow was used to enhance heat transfer. In this study, a numerical methodology is developed to unveil the flow structure induced by the corona discharge and electrode vibration. The oscillatory movement of the electrode is modeled as a cantilever beam vibrating at its first resonant mode. The electric and flow fields are solved by the finite volume methods (FVMs). It is shown that a jet-like flow is generated by the electric discharge. The oscillatory movement of the jet results in flat temperature profile in comparison with the corona only system. Owing to the unsteady characteristic, the jet strength is less strong than that without vibration. The calculated results are qualitatively in line with the experiments, though some considerable differences exist. It is found that the oscillatory flow brings about lower overall heat transfer effectiveness than that without vibration regardless of the corona voltage. On the contrary, experiments showed that heat transfer is enhanced at low corona voltages where the ionic wind is not so overwhelming. The disagreement is mainly attributed to the two-dimensional (2D) assumption made in the simulation. The experimental arrangement, the corona discharge, and the vortex flows resulted all are three-dimensional (3D). Therefore, 3D calculations become necessary.