## 2 Computational Framework
### Present Investigation Case  
The model used in the current study was based on the flying wing MAV developed at the University of Sheffield [8; 28]. This model is composed of a Zimmerman planform wing, a fuselage, a vertical stabilizer, and a propeller in a tractor configuration. The model is shown in Figure 3c with a coordinate system with x in the chordwise direction, y normal, and z spanwise. The wing has a mean aerodynamic chord of 0.221 m and an aspect ratio of 2.12. The freestream speed is 8.4 m/s, and the corresponding Reynolds number is 1.3 \(\times\) 10\({}^{5}\). The airfoil used in this investigation was a simple cambered thin airfoil, as shown in Figure 3b. It included both positive and negative cambers and the relevant parameters are listed in Table 2. The positive camber was designed to have better aerodynamic performance whereas the reflex camber was designed to maintain stable level flight, resulting in decreased flight times. Not only the static stability but also the dynamic stabilities (for control handling) were important for the design. Similar to [PERSON] and [PERSON] [9], the lift center location was calculated from the normal force and pitching moment taken from the  
Figure 2: Mesh topology and aerodynamic coefficients for wing planform, (**a**) C-H mesh topology, (**b**) mesh at leading-edge, (**c**) O-grid mesh topology, (**d**) spanwise mesh spacing, (**e**) lift coefficient, (**f**) drag coefficient. \(\overline{c}/4\) location of the wing. Although the location of lift center was close to \(\overline{c}/4\) point at low angles of attack, it shifted towards the trailing edge as the incidence increased. The reason behind this is from both the increasing trailing edge separation and the strengthening wing tip vortices. In this investigation, the mean aerodynamic chord, \(\overline{c}\), was used (Figure 3a). The wing had a constant thickness of 2 mm and the shape of the cross section was rectangular with no sharp leading- and trailing-edge, and the airfoil is shown in Figure 3b. The camber was defined as maximum convex camber (h\({}_{1}\)/\(\overline{c}\)), maximum concave and reflex camber (h\({}_{2}\)/\(\overline{c}\)), maximum concave camber location (d\({}_{1}\)/\(\overline{c}\)), and the maximum reflex camber location (d\({}_{1}\)/\(\overline{c}\)); further details are shown in Ref. [11]. Considering the MAV configuration, the fuselage was a substantial component to accommodate the payload and propulsion devices, such as battery, motor, and servos, etc. Figure 3d shows the fuselage dimension for our model. It had a front height, h\({}_{t}\), of 0.059 m, rear height, h\({}_{t}\), of 0.021 m, and a total length h\({}_{L}\) = 0.216 m (Table 2). This design of the fuselage was dictated by the size and placement of the components. The fuselage layout affects the center of gravity margin and hence the static stability. For this purpose, the battery was designed to be movable to adjust the center of gravity. Another interesting point is how the fuselage affects the overall aerodynamics. [PERSON] [29] simulated the fuselage and wing separately and the relevant aerodynamic forces are shown and discussed. However, the authors did not mention anything about the interaction between the wing and the fuselage. [PERSON]'s [30] numerical results showed MAV with fuselage \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**MAV model**} & \(\mathbf{d_{t}}\) (d\({}_{t}\)/\(\overline{c}\)) & \(\mathbf{h_{f}}\) (h\({}_{t}\)/\(\overline{c}\)) & \(\mathbf{h_{L}}\) (h\({}_{L}\)/\(\overline{c}\)) & \(\mathbf{h_{t}}\) (h\({}_{t}\)/\(\overline{c}\)) & \(\mathbf{t}\) (t/\(\overline{c}\)) \\ \cline{2-5}  & 0.068(31.7\%) & 0.059(26.6\%) & 0.216(97.6\%) & 0.021(9.49\%) & 2e\({}^{-3}\)(0.93\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Propeller location and fuselage specifications.