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divergence free random field

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Old   October 18, 2017, 07:54
Default divergence free random field
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Dear all
I am currently working on the development of hybrid RANS/LES for the transition of turbulent boundary layer (using Openfoam). I am planning to generate some random number at the beginning of the transition. The problem is that the random number is not divergence free, and makes the velocity field non-divergence free, since I am adding it to my velocity field after pressure correction, where is already divergence free.
I have playing with different way to generate div-free random number but not successful, like

1- U' = curl (grad(f), grad(g)) ...... f and g are random numbers.
2- U' = f_solenoidal +f_dilatation .... f is random number vector.\
I believe the reason that they don't work is related to collocated grid in Openfoam (I am new and my knowledge about Openfoam is limited), which causes inaccurate interpolation when one wants to compute the discrete divergence.
Any help is highly appreciated.
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Old   October 18, 2017, 09:22
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You can work doing the random generation for two components and computing the third one from the Div v =0 constraint.

Differently, you could compute a divergence-free vector field from the Hodge decomposition
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Old   October 18, 2017, 10:50
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Try following this:

https://www.researchgate.net/publica...blicationTitle

and the citations therein. Maybe you can find something suitable to your needs.
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Old   October 18, 2017, 11:07
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Quote:
Originally Posted by sbaffini View Post
Try following this:

https://www.researchgate.net/publica...blicationTitle

and the citations therein. Maybe you can find something suitable to your needs.

Yes, the method described in the paper is nothing else that a form based on the Hodge decoposition
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