TRANSONIC FLOW FOR THE NACA_12 WING:

        In this part, we are going to talk about the behaviour of airflow wing NACA_12  with an incoming transonic flow(Mach=0.85).We used  an unstructured grid for this simulation.This study show the differents caracteristics  for the  flow with differents attack angles.In the second time we present the effect of this evolution in the  pressure-coefficient (Kp) and the coefficient lift .
 

    1) THE UNSTRUCTUCTURED GRIDS:

       In AVBP, we can use for meshing,stuctured and unstructured grids.For this simulation we used the second one
who can take different polygons.The unstructured grids give a lot of flexibilities for complex configurations but require
to add storage for the list of element to vertex pointers and an overhead for first looking up the number of the forming nodes in the table  before loading the corresponding solution values(indirect addressing).The mesh generation algorithms for triangular and tetrahedral meshes for Euler are robust and mostly automated.
 

Grid for NACA_12 simulation
 
 2)THE NACA_12 SIMULATIONS:

We present and analyse the isopressure simulations because the distribution of pressure create the lift force.

Attack Angle_0:
 



 



 
 




Criterion convergence for all simulation is around 10-7
 

INTERTPRETATION:

        In general analysis we can say and see we have a shock wave for each incidence angle and this wave move on the extrados wall.For the Angle_0 we have two shock waves and they are antisymmetric,it is the fact we are an attack and a wing symmetric.For the other angle until the take down we have the shock in antisymmetric with attack angle.
After the "take down "(Attack Angle_25)we have a distribution of the pressure  very differente,in the attack edge a great pressure density and near the leak edge a great loss pressure.This importance difference occurs "the take down".
 

DISCUSSION:
We can say in the first time  we obtained goods results for the incoming transonic NACA_12 simulation .We have a shock for a transonic flow like the theory  and the differents experiences.But we obtain a take down point at 25 degrees whereas we should have around 17degrees.This fact is that we do not worry about the layout boundary.
In did  our simulation  resolve the Euler equation.In perfect fluide,there is a solution for Euler equation
drawing the flow around an obstacle.This solution is an approximation of  the Navier-Stokes equations available
almost everywhere in stead of near the wall.And too AVBP code  treate the Euler equation with a good precision,that why we can represent the behaviour of the wing in differente flow.