Orthogonality in Gas Project Non Divergent Node

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Hello everyone.
I encounter a weird problem.
As you know Gas Project Non Divergent nodes use the Helmholtz-Hodge decomposition to decompose a velocity field into a pressure scalar and a divergent free vector fields.
The gradient of pressure and divergent free vector field should be orthogonal to each other but when I look at the volume trail they are not orthogonal in any way!
No matter how hard I crank up the resolution the result is always the same.
The red lines are divergence-free portions and the green ones are curl-free portions.
I also attached my project in case anyone wants to look at it.
Does anyone have any solution to this problem?
Thank you so much.
Edited by N-G - 2023年5月9日 20:07:22

Attachments:
Projection.png (582.2 KB)
Vector Field Decomposition SideFX.hip (152.6 KB)

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I'm also confused but I have a few thoughts:

- I don't trust the gradient calculation, I never have. Something's not right about it but I don't know what. You can easily get weird results.

- That aside, I don't trust the vector calculations (advect) and the viewport so I did a little test where calculate the dot product. They hover neatly around 0, as they should. The vectors however don't always look right.

- Maybe something with face vs center sampling might interfere but sometimes I can't calculate a gradient at all out of it.

So, I don't know but I have a feeling Houdini isn't telling us the truth.

I attached a file.

Attachments:
Vector Field Decomposition SideFX.hiplc (187.2 KB)

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Soothsayer
I'm also confused but I have a few thoughts:

- I don't trust the gradient calculation, I never have. Something's not right about it but I don't know what. You can easily get weird results.

- That aside, I don't trust the vector calculations (advect) and the viewport so I did a little test where calculate the dot product. They hover neatly around 0, as they should. The vectors however don't always look right.

- Maybe something with face vs center sampling might interfere but sometimes I can't calculate a gradient at all out of it.

So, I don't know but I have a feeling Houdini isn't telling us the truth.

I attached a file.

Thanks a lot.
You know the real reason behind the zero dot product is that the lengths for the pressure gradient vectors are too small.
If you normalize both divergence-free and pressure-gradient fields you will see the dot product is not going to be zero anymore!
As you visualized both divergence-free and pressure-gradient fields they are not orthogonal in any way!
I also tested it with VDB project non-divergent node with no luck!
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