NACA 12 profile, using a coarse mesh :


This mesh is quite coarse (4000 cells), allowing a shorter iterating time.







The simulations were done in a supersonic state, with an incoming flow at Mach 1.2. The solution is calculated using the Euler equations. These equations are very simplified, and the simulation is not expected to give correct results at high angl of attack. The phenomenas apearing in the boundary layer (develloped with the Navier-Stokes equations) are crucial in the stall of the plane, and are not captured here.

The first simulation done was at an angle of attack of 7 degrees. This converged quite quickely. The residuals were 10^-5 in 2000 iterations, and 10^-9 in 5000 iterations.







The results given by this simulation appear quite good. There is a shock-wave in front of the wing, and an under-pressure on it's upper face.
 
 

This gives an undimensionnal pressure along the wing of (projected on the vertical axis):
 
 







Integrating this gives the lift of the airfoil, here : 0.4768.

This lift is evaluated the same way for different angle of attack. The same thing is done for the drag, and the results observed are (drag is green, lift black) :

This gives a polar :

It is to be noticed that most simulations were done until the residuals were at around 10^-6, and that the result given at a 7 degrees angle of attack is quite different from the others, even though it is hard to tell if it is better or worse than the others. As a metter of fact these results seem to be false.  Wings should stall before 18 degrees, and here it continues to lift. This is probably due to the use of the Euler equations, as was predicted. The results near a 0 degree angle of attack are to be compared to other simulations with other meshes, in order to validate them, having no experimental data.