In this part of the project, the study has been made with the test-case Bump which will be describe later. We have tested particularly the influence of two parameters: the CFL number and the artificial viscosity.
Their influence will be evaluated by looking at convergence of each different calculation.

        The Bump test is a computation on half profile whose geometry is showed in the next figure representing
the mesh used for the calculation:

Unstrctured mesh used in Bump calculation.

        Tests were made with the Mach incidence number taken equal to 0.85 in every calculation.
The following figure represent the shock on the bump in one of our tests:

Mach number evolution on the bump.

        We will now study the influence of the cfl number and of artificial viscosity.

        The cfl number represent the comparison beetween (V+c)*dt and dx (with c the sound speed). This
adimensional number is very important for the calculation. We have made two tests in order to study its influence on
the calculation. The following figure shows the results we have obtained with two different cfl numbers.

            This figure shows that an increase of the cfl number improves the calculation speed. This result was expected. However, it is impossible to increase the cfl too much because it has a limit. Upper that limit the computation may diverge.

        The artificial viscosity is a specific numerical parameter which allows to improve calculation. However,
this is not a physical parameter representing the phenomenom. Therefore it must be chosen with precaution.
The following figure represents two tests with different artificial viscosities.

        By looking at this figure, we can easily conclude that an increase of artificial viscosity improves the
convergence of the calculation (about two orders in precision in this case). Nevertheless, a too high artificial viscosity may disturbs the reality of the physical problem. During the next tests, we will use an artificial viscosity
equal to 0.2 because its precision appears efficient for our studies.