[CarlosLozano]

Hi everyone,
I wonder if anyone has had experience comparing SU2 adjoint solutions at airfoils profile for different mesh refinement. In the attached figure I plot the surface value of the density discrete adjoint variable for drag on 5 different triangular meshes (each one obtained from the previous one by uniform refinement) for inviscid NACA0012 flow with M = 0.8 and aoa = 1.25.
(the solution has not been obtained with SU2 but with DLR's Tau code; I'm trying to see if anyone has had this kind of experience with SU2).

Continuous adjoint shows similar trends, and the sensitivities are OK (they do not show the same lack of mesh convergence as the surface adjoint values).

Any comments would be appreciated.
Regards,

[CarlosLozano]

Hi,
it appears that SU2 has this very same issue, so it must be something inherent in the adjoint equations (probably linked to the adjoint singularity at the trailing edge).

[talbring]

Hi Carlos,

I don't really understand the issue here. Can you elaborate more on that ? Is mesh 0 the finest or mesh 4 ? What other behavior would you expect ?

Regards,
Tim

[CarlosLozano]

Originally Posted by talbring

Hi Carlos,

I don't really understand the issue here. Can you elaborate more on that ? Is mesh 0 the finest or mesh 4 ? What other behavior would you expect ?

Regards,
Tim

Hi Tim,
mesh 0 is coarsest. The issue here is that, in principle, as you refine the mesh you should expect that the computations would converge to a result, not change continually as the mesh is refined. When this happens, as in this case, you have to understand why. it can either be a bug (which I believe can be ruled out now since two different codes give simialr results) or a more fundamental issue. When I first posted the comment I hadn't done the computations with SU2 yet, so I wanted to check if some SU2 user had experienced the same "problem". Now I positively know that SU2 yields the same result, so the post can serve just to point out that this apparently odd behavior IS the one to expect. I believe this is related to the numerical adjoint system, which is afected by the singularity at the trailing edge. Inviscid adjoints are generically singular at trailing edges (meaning that the analytic solution has an infinite value there). In the discrete solution this is reflected in the growing values of the sirface adjoint near the trailing edge as the mesh is refined. These increasingly larger values probably corrupt the adjoint solution throughout the airfoil profile, causing the mesh divergent behavior we see.

[fpalacios]

Hi Carlos,

The discrete adjoint in SU2 uses AD (it is not a manual implementation of the discrete adjoint) and the entire code has been differentiated. It would be interesting to check if you have the same problem with the AD in SU2.

Best,
Francisco

BTW Continuous adjoint is not the preferred option in SU2. However, there have been a lot of progress trying to understand the limitation of the surface formulation vs. domain formulation. If you are interested in collaborate with us feel free to use GitHub (pull request) or take a look at the SU2 IDS (www.su2devsociety.org)