Influence of the artificial viscosity

In the AVBP code, the numerical scheme
used is centred. In certain cases of discontinuity, such as shock for example,
this scheme is not appropriate. That is why, there is the possibility of
adding a term in the equations to make the numerical scheme able to solve
the problem. This term is controlled by a coefficient called the artificial
viscosity. For a value of 0.5, the numerical scheme become an upwind.

The problem of this term is that the resulting scheme
introduce more dissipation that the original centred scheme. In order to
limit this imprecision, a censor detect the zone where there is is high
gradients (close to discontinuity) and modify the original centered scheme
only in this zone.

To study the influence of the artificial viscosity, we have computed two similar cases, i.e. Mach=1.5, no incidence, with different censors. In one case, the censor is normally active in high gradient zones, in the other case, the censor is always active. It means that in the last case, a (more) dissipative scheme is used in all the domain.

If we compare the residuals for both
case, the differences are very small.

Here follows the variation of the residuals with the
number of iterations. In red the dissipative case, in black dotted the
"normal" calculation.

And now zoomed:

If the difference is not flagrant for the residuals, it is not true when we visualize the flow. If we compare the Mach number for example, we can see some differences, especially in the high gradient zone behind the engine. The high Mach number zone (in red) is not as visible in the dissipative case.

Normal computation

Dissipative case

Remark: Even if the colour scale are not exactly the same,
these pictures can give us a good idea of the the influence of the artificial
viscosity.

We have several calculation at Mach=1.5 for different
incident angles. For each of them, we have calculated the Mass flow rate
inside the engine.

The following graph shows a comparison between solutions
where the censor is always activated (red) and solution with a normal censor
(blue).

As for the residuals, the differences are quite small.