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discretization of convective terms of Spalart Allmaras equations 

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March 28, 2019, 06:34 
discretization of convective terms of Spalart Allmaras equations

#1 
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Abolfazl
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Hi everyone.
I'm about to discretize the spalart allaras equation and add it into my compressible code based on Roe scheme. I was wondering can i use a simple first or second upwind for discretization of convective terms of spalart allmaras like incompressible flow or I should use the method of Roe!? thanks a lot 

March 29, 2019, 01:53 

#3  
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Abolfazl
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Quote:
Actually I don't know. I know how i can use forward and backward discretization for convective term of spalart and this is all I know. I have no idea how I can use Roe for spalart! actually maybe I'm not asking the right question. I'm not well familiar with turbulence models. 

March 29, 2019, 05:00 

#4 
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Well, I tougth that, as you have a Roe scheme in your compressible code, you kind of knew it. For a general vector equation of the form:
your Roe scheme for the flux at the interface between cells L and R typically is: where: is the Jacobian of the flux (upwind altered by taking the absolute eigenvalues), the surface normal is assumed to point toward the R cell and the L and R states can be, in general, cell values (1st order) or suitably reconstructed values (2nd or higher order). Now, if you apply this to a scalar equation for with assigned mass flux, say , which is the first component of above, you get as flux: which actually is the upwind scheme in its most common version. In layman's terms, the point is that, for a scalar equation, you don't have a wave structure anymore, just a single eigenvalue, . 

April 7, 2019, 08:48 

#6  
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Abolfazl
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Quote:
thank you for your kind reply. I checked the "computational fluid dynamics Vo.II" written by Hoffmann. I found that I can discrete the convective terms using a simple upwind scheme. but now I have another question. there is a term in Spalart Allmaras model: ? I know is but I don't get it how i can expand ! is the expansion for 2D like this? ? How like is the expansion for 3D? thanks a lot! Last edited by Abolfazl_cfd; April 7, 2019 at 13:01. 

April 7, 2019, 11:46 

#7 
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Filippo Maria Denaro
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Quote:
No, Sij is the symmetric part of the velocity gradient. But what is more, stands in that fact the a turbulence model for incompressible flows does not necessarily can be extended as it is to compressible flows. Have a look here http://iccfd.org/iccfd7/assets/pdf/p...1902_paper.pdf 

April 7, 2019, 15:29 
Discretization

#8 
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Selig
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Unless you absolutely need to use the Roe scheme, I would suggest the AUSM+ scheme (or one of the variants.) It's easier to implement, cheaper in computational cost, and can be more accurate than the Roe scheme (I can't think of a case of where it's not.)


April 8, 2019, 02:54 

#9  
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Abolfazl
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Thank you for correcting my mistake. I toke a look into the paper and found it really helpful. specially the part about negative values of source term in Spalart Allmaras. Thank U. 

April 8, 2019, 02:59 

#10  
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Abolfazl
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Thank you for your precious advice. Actually I am working on immersed boundary method. years ago I tried to add my immersed code to a AUSM solver but some instabilities near the immersed boundary started to grow and after several attempts I gave up upon AUSM. But for Roe scheme it works properly. Thanks a lot. 

April 9, 2019, 03:47 

#11  
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Abolfazl
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Quote:
finally I could write the spalart allmaras code. Although instead of Roe scheme, I used ECUSP scheme, but the results in channel flow in Re=10000 are satisfactory. If anyone need the code, can send me an email. I would happy to share it and I hope it would help. moosavi.abolfazl@gmail.com 

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