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Heat flux to rotated solid at ambient conditions
This test case contains two solid slabs, one conforming to the grid and one at a 45 degree angle. There is no heat source and I expect everything to remain at 20 C. It's close, but the rotated slab has an incident heat flux of 0.411 kW/m2 rather than the expected 0.419 kW/m2 like the non-rotated slab. This is not a big problem, but I wonder if this is the result of the sum of solid angles not reaching 2 pi for whatever reason. If this can be fixed easily, let's do it. If it's just a result of the nature of the way the unit sphere is discretized, that is OK too. I just want to understand.
Quite sure it is related to the control angle borders. Worrying thing is that we get lower heat flux on both sides, i.e. energy is not conserving.
This is a perfect 45 degree rotation. Could this possibly be due to some "less than or equal to" logic? Like I said, this is not a big issue, but it might reveal a simple oversight.
There are two types of errors: (1) 'less than 0.0 logic', as you guessed. (2) angle overhangs. WHen 2pi hemisphere of the wall does not align with control angle boundaries, the simple criterion (DLN > 0) does not mean that all directions within the control angle would be out of the wall. When wall cuts through the control angle, part of the angle is out of the wall, part is into the wall. Accurate calculation would require cutcell-wise calculation of DLNs. Dot product is not the same.
I will try to fix (1) first, because it is just logic. Then we see how much inaccuracy is caused by (2), which is much more fundamental problem.