# 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 New Member   Abolfazl Join Date: Oct 2016 Posts: 28 Rep Power: 8 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 28, 2019, 07:47 #2 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,087 Blog Entries: 29 Rep Power: 38 How would you define the Roe method for a scalar equation as the one for SA and how an upwind scheme? They are the same for, say, unstructured schemes

March 29, 2019, 01:53
#3
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Abolfazl
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Quote:
 Originally Posted by sbaffini How would you define the Roe method for a scalar equation as the one for SA and how an upwind scheme? They are the same for, say, unstructured schemes
Hi sbaffini

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 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,087 Blog Entries: 29 Rep Power: 38 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, . Abolfazl_cfd likes this.

 March 29, 2019, 05:23 #5 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,087 Blog Entries: 29 Rep Power: 38 Note that I assumed that you are solving the SA equation as decoupled from the main equations, as otherwise you have no option for the scheme. Abolfazl_cfd likes this.

April 7, 2019, 08:48
#6
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Abolfazl
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Quote:
 Originally Posted by sbaffini Note that I assumed that you are solving the SA equation as decoupled from the main equations, as otherwise you have no option for the scheme.
Dear sbaffini

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:
 Originally Posted by Abolfazl_cfd Dear sbaffini 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 the strain rate tensor and 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!

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 Senior Member   Selig Join Date: Jul 2016 Posts: 213 Rep Power: 9 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.) Abolfazl_cfd likes this.

April 8, 2019, 02:54
#9
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Abolfazl
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Quote:
 Originally Posted by FMDenaro 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
Dear FMDenaro
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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Quote:
 Originally Posted by selig5576 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.)
Dear selig5576

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:
 Originally Posted by Abolfazl_cfd 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
Thank U all.

finally I could write the spalart allmaras code. Although instead of Roe scheme, I used E-CUSP 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