## 1 Introduction
During the positive half cycle, the upper electrode functions as the cathode, and the dielectric material covers the lower electrode and works as a pseudo-anode. Because of the dielectric material and asymmetric electrode configuration, the plasma formation is relatively low during the negative half cycle. A detailed description of plasma formation and the induced body force mechanisms was described in [11; 12]. There are fundamentally two methodologies to numerically model a DBD plasma actuator:  
Figure 1: Schematic of a DBD plasma actuator. First principles based models  
Phenomenological or simplified models  
First principles based modeling approaches are classified as fluid models, kinetic models, or hybrid models. These models are accurate for capturing plasma physics and near wall physics. There were several publications that investigated the use of plasma actuators based on first principles based models [13; 14; 15; 16; 17]. On the other hand, phenomenological models focus on the bulk effect of the plasma on the flowfield. These models are popular due to their simplicity of modeling and implementation. There are several validated phenomenological models that are used to model plasmas. Among the most popular are the [PERSON] model [18], the Suzen and Huang model [19; 20], the [PERSON] model [21], and the lumped-element circuit model [22; 23]. Following [PERSON]'s work, research was conducted showing the effective use of DBD plasma actuators on airfoils, hump models, bluff bodies, compressors, rearward facing steps, and flat plates. Additional studies, such as [PERSON] et al. [19], studied on the effect of a DBD plasma actuator on PAK-Bblade flow separation and a low-pressure turbine flow with large flow separation in a quiescent environment [20]. [PERSON] et al. [24] and [PERSON] et al. [25] studied DBD actuators to control flow separation over a NACA 0015 airfoil at a high angle-of-attack, showing the ability of phenomenological DBD actuator models to control low-speed flow. [PERSON] et al. [26] studied a DBD plasma actuator model with a correction factor to examine the complex flow structure. [PERSON] et al. [27] used the marker and cell (MAC) based predictor-corrector method to simulate plasma induced electro-hydro-dynamic (EHD) flow and validated their numerical findings with experimental results. [PERSON] et al. [28] conducted experiments of DBD plasma actuators to control external and internal flow separation over a hump and compressor cascade, respectively. A creative stair-shaped DBD plasma actuator configuration was introduced by [PERSON] et al. [29] to increase induced flow velocity and mechanical efficiency with an acceptable actuator durability. [PERSON] et al. [30] showed that DBD plasma actuators can effectively reduce the drag and increase the lift. [PERSON] et al. [31] studied the effects of DBD plasma based control on turbulent separation on a rear facing ramp. [PERSON] et al. [32], [PERSON] et al. [33], [PERSON] et al. [34], and others studied the effects of DBD plasma actuators on the NASA hump model. The Shyy model, proposed by [PERSON], was adapted for use in this work due to the reasonable accuracy, low computational cost, and simple implementation [24]. The details of this model are presented in the Computational Methodology Section.