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Is it possible to use divergence theorem to compute the pressure gradient on a face? 

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April 5, 2023, 00:44 
Is it possible to use divergence theorem to compute the pressure gradient on a face?

#1 
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pengfeiguo
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I was reading this really great paper on momentrum weight interplation (Bartholomew P, Denner F, AbdolAzis M H, et al. Unified formulation of the momentumweighted interpolation for collocated variable arrangements[J]. (Journal of Computational Physics, 2018, 375: 177208.).
It has been enjoyable and rewarding until I came across Eq. (71). How is it possible to apply the divergence theorem on one surface? Is this a typo? A screenshot of the formula is here : http://www.aliyundrive.com/s/F7HCnF6u6RH Maybe it is a typo? Any suggestions are welcome. Thanks. Last edited by pfguo; April 5, 2023 at 02:34. Reason: correct divergence 

April 5, 2023, 05:19 

#2 
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Arjun
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Don't have access to the paper nor have read it but usually for this type of integration the single cv is considered that is union of the two cvs on either sides of face.


April 5, 2023, 08:43 

#3  
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Filippo Maria Denaro
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Quote:


April 5, 2023, 10:01 

#4 
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pengfeiguo
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April 5, 2023, 10:03 

#5 
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pengfeiguo
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Yes, two cell centers P and F both appear in the equation, I am really confused.
Last edited by pfguo; April 5, 2023 at 10:04. Reason: correct english words 

April 5, 2023, 13:02 

#6 
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Filippo Maria Denaro
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I cannot read now the paper, however I mean that
Grad p = div (Ip) > Int[V] div (Ip) dV = Int[S] np dS Grad p = lim V >0 1/V Int[S] np dS 

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divergence, gradient scheme 
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