__First steps in Aerodynamics __

__with CFX TASCflow__

**IV. Supersonic flow**

A initial Mach 2 flow is going to be simulated in this part, using as initial guess the solution of the Mach 0.8 flow. Two scheme will be checked : the modified linear profile scheme and the upwind difference scheme, which is one of the most basic ones.

1. Modified linear profile |

The modified linear profile is a scheme based on the finite volume method, but the calculation of the transfers
are complicated because of an other fragmentation of the basic volume element. We will check the ability of this scheme
to solve a shock wave : meshes number of the shock repartition and quality of the shock description.

Some problems of numerical stability appear directly upstream of the shock wave (which is attached to the profile). In fact, this scheme creates too much numerical dissipation, but the shock is well localised and is not strained a lot.

2. Upwind differences |

The first difference it's possible to show between the two schemes is that the calculation with the upwind differences
are really longer than the previous ones, as the residuals evolution graph proofs.

Then, we can verify that the upwind difference scheme permits to smooth the solution compared to the result graphs of the previous part. The numerical stability problems, represented by circles placed directly upwind the shock wave in this case, are reduced. Although the shock wave is also smooth, the solution is not really far from the precedent one.