Accuracy of RANS solution close to sharp edges
Dear community,
I have a rather general question regarding the resolution of edged geometries by discrete meshes and the corresponding experience in the community. Some background: I use an academic RANS code (finite volume, unstructured, parallel, multiphase, etc.). We are in the situation, that we need RANS solutions of quite high quality. By that I don't refer to integral values, but the quality of the flow field close to feature lines / edges that are perpendicular to the main flow direction (like a backward facing step). In my experience, such features can lead to quite unphysical values in the cells directly adjacent to the edge. When calculating the gradients of the flow field the situation gets even more tricky... I understand, that even in experiments one would expect rather high gradients in the vicinity of such edges. This remains as some kind of an inherent problem when one tries to resolve the sharp edge in a discrete manner by generating a mesh of finite resolution. In the recent past, I've tried to figure out how other groups / codes handle this issue. Unfortunately it is quite difficult to find any related information. I would very much appreciate if someone would like to share her/his experience or can give me a hint where to find related information in the literature. Best regards, tvd 
I don't know if i got your point but, my very personal point of view is that it has little sense (if any at all) to look at this very specific flow features at this small geometrical scale when using a RANS/URANS modeling approach, less than ever if your numerical accuracy is typical of RANS/URANS codes.
In my opinion it is the same as looking for a very accurate wall stress when using a wall function approach, it isn't really part of the game. Besides this, even when using a DNS approach, still remain the problems you mentioned and i think that in some cases there may also be some issues related to the wellposedness of the problem (but more mathematically oriented people can say more on this). 
Even the solution of Poisson equation would have singular behaviour near corners. It obviously does not represent reality. So it may not be worth worrying about this. If you can figure out the singularity analytically, then you can subtract that out and try to compute the remaining nicely behaved part of the solution numerically. I think people have done such things for lid driven cavity problem which also has corner singularities.

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