## 4 Experiment and Results
### Numerical Experimental Results
#### 4.2.2 Airfoil Computation Results  
The computation area when calculating the flow around the 2D NACA0012 airfoil is shown in Figure 11. \(C\) is the airfoil length, and \(C=400 dx\), where \(dx\) is the grid size. The entire computation comprises 200 million grids. A velocity boundary condition and non-equilibrium extrapolation boundary condition are respectively used on the inlet boundary and outlet boundary. The standard bounce back boundary condition is used for the upper, lower, and airfoil edges [14]. The inflow Mach number M = 0.1, the Reynolds number Re = 1000, and a total of 1 million time steps are calculated; and the angles of attack are calculated as \(0^{\circ}\), \(4^{\circ}\), \(6^{\circ}\), \(8^{\circ}\), \(10^{\circ}\), \(12^{\circ}\), \(15^{\circ}\), \(17^{\circ}\), \(20^{\circ}\), \(22^{\circ}\), \(25^{\circ}\), and \(28^{\circ}\). Figures 12 and 13 show the pressure and velocity clouds at several representative angles of attack with angles of attack of \(0^{\circ}\), \(4^{\circ}\), and \(8^{\circ}\) and \(12^{\circ}\), \(15^{\circ}\), and \(20^{\circ}\), respectively. It can be seen from Figure 12 that the flow tends to be stable for angles of attack of \(0^{\circ}\) and \(4^{\circ}\), and there is no flow separation phenomenon, which is consistent with the literature [21, 22, 23]. When the angle of attack is \(8^{\circ}\) or higher, unsteady vortex shedding occurs after the airfoil tail, and, as the angle of attack increases, the vortex shedding becomes more obvious than before and the flow instability becomes larger. It can also be seen from Figures 12 and 13 that, with an increase in the angle of attack, the pressure difference between the lower side and the upper side of the airfoil increases gradually; therefore, it can be qualitatively known that the lift coefficient will also increase, which can be understood as the vortex lift generated by the shedding vortex. Figure 11: Computation area. The left side is the inflow and the right side is the outflow. Figure 10: (**a**) Acceleration ratio and efficiency with computing processing elements (CPEs); (**b**) Mega Lattice Site Updates Per Second (MLUPS) with CPEs. In order to further quantify the main characteristics of the flow and evaluate the aerodynamic performance of the airfoil, the lift coefficient \(C_{L}\) and the pressure coefficient \(C_{p}\) of the upper and lower surfaces of the airfoil are calculated, respectively, as  
\[C_{L}=\frac{F_{L}}{\frac{1}{2}\rho_{0}u_{0}^{2}C},\qquad C_{p}=\frac{p-p_{0}}{ \frac{1}{2}\rho_{0}u_{0}^{2}},\]  
where the subscript \(0\) represents the value under far-field conditions, respectively, \(C\) is the size of the airfoil, and \(F_{L}\) is the lift, i.e., the vertical component of the aerodynamic force acting on the airfoil chord. Figure 14a shows the average pressure coefficient distribution of the upper and lower surfaces when the angle of attack is \(8^{\circ}\). Owing to the angle of attack, the average pressure coefficients for the upper and lower surfaces are different at the front of the airfoil, and they gradually change with the position; this appears to be a consistent trend. The trend and the extreme value of the computation result are in good agreement with those in the literature [22], and a mean error less than \(1.5\%\). Figure 14b shows the trend of the lift coefficient as a function of the angle of attack. This result is also in good agreement with the results in the literature [24], and a mean error less than \(5\%\). Once the angle of attack is greater than \(25^{\circ}\), the vortex may be broken, and the lift coefficient is reduced; this result agrees well with the critical angle of the stall phenomenon in [25]. Figure 12: Pressure and velocity clouds at different angles of attack: (a) pressure distribution on the upper side; (b) lower right side of the foil. The angles of attack are \(0^{\circ}\), \(4^{\circ}\), and \(8^{\circ}\) (left to right).