# divergence free random field

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 October 18, 2017, 07:54 divergence free random field #1 Member   SAM Join Date: Apr 2012 Posts: 66 Rep Power: 10 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.

 October 18, 2017, 09:22 #2 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 5,389 Rep Power: 57 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 hnemati likes this.

 October 18, 2017, 10:50 #3 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 1,276 Blog Entries: 19 Rep Power: 30 Try following this: https://www.researchgate.net/publica...blicationTitle and the citations therein. Maybe you can find something suitable to your needs. FMDenaro and hnemati like this.

October 18, 2017, 11:07
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Filippo Maria Denaro
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Quote:
 Originally Posted by sbaffini 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