[CarlosLozano]

Hi everyone,
I wonder if anyone has had experience comparing surface values adjoint solutions on airfoil profiles 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 been obtained with DLR's Tau code; I'm trying to see if anyone has had this kind of experience).

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,

[naffrancois]

Hello,

Could it be an issue in the mesh quality evolution as the refinement cycles increase ? If by uniform refinement you mean that each segment is split in two, is there a strategy to move airfoil surface nodes to account for the real geometry ? Also, if no smoothing is applied at each uniform refinement cycle, I would expect that the worst distortion present in the base coarse mesh is still there unaltered in the finer grids and eventually becomes the biggest source of truncation error.

I would try to generate a sequence of independent meshes from the mesh generator checking that the quality metrics do not decrease. These are my two cents, I do not know much about adjoint methods.

Good luck !

ps: you are talking about inviscid, so I guess you are not using hybrid meshes. At the time I used tau code, uniform refinement of the structured layer was only available in the normal direction yielding very stretched elements at the transition with triangles.

[CarlosLozano]

Originally Posted by naffrancois

Hello,

Could it be an issue in the mesh quality evolution as the refinement cycles increase ? If by uniform refinement you mean that each segment is split in two, is there a strategy to move airfoil surface nodes to account for the real geometry ? Also, if no smoothing is applied at each uniform refinement cycle, I would expect that the worst distortion present in the base coarse mesh is still there unaltered in the finer grids and eventually becomes the biggest source of truncation error.

I would try to generate a sequence of independent meshes from the mesh generator checking that the quality metrics do not decrease. These are my two cents, I do not know much about adjoint methods.

Good luck !

ps: you are talking about inviscid, so I guess you are not using hybrid meshes. At the time I used tau code, uniform refinement of the structured layer was only available in the normal direction yielding very stretched elements at the transition with triangles.

thanks a lot for your reply. I'm using triangular meshes, and unifor refinement means that each triangle is dividided into 4 (yes, each segment is divided in half). i don't think the new nodes not exactly following the airfoil geometry is the issue hre, as cp curves, for example, behave much more smoothly. The issue here (the mesh divergence of surface adjoint values) is an intrinsic problem with inviscid numerical adjoint solutions which is caused by the adjoint singularity at the trailing edge. As the mesh is refined, nodes get closer to the trailing edge and, thus, to the singularity, resulting in larger and larger values of the adjoint towards the trailing edge. This in turn, probably corrupts the adjoint solution throughout the airfoil profile producing the mesh-divergent behavior that we observe.