## 2 Simulation Setup  
### Geometric Model Selection  
In order to approximate the authentic operating conditions of low-altitude flight for MAVs, numerical simulations employed air as the flowing material, with an environmental temperature of 298.15 K and an atmospheric pressure of 1 atm. For fixed-wing MAVs, the selections of airfoils often lean towards well-established low-speed airfoils. Therefore, the NACA2412 airfoil (chord length, \(c=100\) mm) was chosen. This particularly non-symmetric airfoil exhibits superior aerodynamic performance even during low-speed flight [32]. The typical Reynolds number for MAVs is on the order of \(10^{5}\)[11]. Considering that the chord length was 100 mm, finally, the incoming velocity was set as 15 m/s, and the Reynolds number for the airfoil was approximately \(1.03\times 10^{5}\), which conferred to the operational conditions of MAVs. The primary objective of this study was to employ transverse grooves to reduce viscous drag, and as such, the grooves were placed in regions of the airfoil surface where pressure drag was slight. To investigate the influence of adverse pressure gradients (APG) on flow, [PERSON] [33] defined the Clauser parameter \(\beta\) to quantify the magnitude of adverse pressure gradients, as depicted in Equation (1). \[\beta=\frac{\delta^{*}}{\tau_{w}}\frac{dP}{dx} \tag{1}\]  
In Equation (1), \(\delta^{*}\) represents the displacement thickness of the boundary layer, \(\tau_{w}\) denotes the local shear stress, and \(dP/dx\) represents the pressure gradient along the streamwise direction (positive for adverse pressure gradients and negative for favorable pressure gradients). This parameter was employed in our study to assess the extent of adverse pressure gradients. Figure 2 illustrates the distribution of \(\beta\) on the suction and pressure surfaces of the NACA2412 airfoil under the aforementioned flight conditions. Due to the tendency for airfoil flow separation at low angles of attack (AOA) under low Reynolds numbers [11], the angle of attack of the airfoil in Figure 2 is merely 2 degrees. It can be observed that near the airfoil leading and trailing edges, both the suction and pressure surfaces exhibit high values of \(\beta\), indicating the presence of large pressure drag in these regions (\(\beta>2\)[34]). To minimize interference and facilitate research, the chord length of the airfoil was evenly divided into four segments, spanning from 20% to 80% of the chord length, and sequentially designated as the \"Front(F),\" \"Middle(M),\" \"Rear(R),\" and \"Tail(T)\" sections. Grooves would be positioned on the corresponding suction and pressure surfaces in these designated locations, as depicted in Figure 3. The adverse pressure gradient in these areas was not significant. For the transverse V-shaped symmetrical grooves, the most critical geometric parameters are aspect ratio (\(\rm{W/H}\)) and depth (H) (shown in Figure 1). When the aspect ratio of the groove is approximately 2, the boundary vortex structure within the groove is most stable, which is conducive to drag reduction [35]. The selection of groove depth was guided by the Transverse Groove Drag Reduction Model [31], which builds upon the stability of boundary vortices, deriving quantitative relationships among the local Reynolds number, groove dimensions, and drag reduction rate from the vortex dynamics. It allows to directly obtain the groove depth corresponding to the highest drag reduction rate based on the local Reynolds number. The derivation process did not fully consider the impact of strong turbulence, and the model only has high accuracy at low Reynolds numbers (\(1.09\times 10^{4}-5.44\times 10^{5}\)), which is suitable for the working condition in our research.