sbaffini |
March 30, 2021 04:59 |
There isn't, to the best of my knowledge, any paper discussing this with the proper theoretical rigor, or probably discussing this at all.
In general, reasoning on the grid resolution alone is not rock solid, for the simple reason that such vortex methods have also a prescribed size , which can be assigned independently from the grid resolution. Also, the vortex positions are random, so you can't actually control anything at the local level as the Nfaces/4 rule might seem to suggest.
One approach I have seen is to use something like:
where you basically assume that, on average, the inlet face is covered by vortices.
You should instead adapt to the grid resolution. But, again, this requires more than simply reasoning on a pure number. Different schemes will require different resolutions, but sometimes a magic number exists that makes things work even if they shouldn't.
So, in conclusion, N is not directly linked to the resolution. Indeed, some have found reasonable solutions with a fixed number O(100).
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