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Second order upwind is not UPwind!!!

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Old   May 22, 2011, 01:40
Default Second order upwind is not UPwind!!!
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http://www.kxcad.net/ansys/ANSYS_CFX.../i1311648.html

It is stated in the CFX theory (above link) that when one selects the high resolution scheme as below

\phi_{ip}=\phi_{up}+\beta\nabla\phi\bullet\bar{r}

\nabla\phi\ is the value at the upwind node.

On the other hand when user selects the specified blend factor for \beta (between 0 and 1), \nabla\phi\ is equal to the average of the adjacent nodal gradients. I wanna know, this scheme is the upwind or central differencing scheme?


http://my.fit.edu/itresources/manual...ug/node992.htm

Where as in fluent user guide (above link) 2nd order upwind scheme is given by following formula

\phi_{f,SOU}=\phi+\nabla\phi\bullet\bar{r}

\nabla\phi\ is the gradient of \phi\ in the upwind cell

Both high resolution (CFX) and 2nd order upwind scheme (Fluent) are based on the principles by Barth and Jespersen [1] so that no new extrema is introduced in the solution, therfore monotonic behavior is preserved.



1. Does it mean that the high resolution scheme of CFX and 2nd order upwind scheme of fluent are equivalent.

2. Does it mean that the CFX 2nd order scheme is more like a baised 2nd order scheme with one term of upwind and 2nd term (anti diffusive term) is central differencing type?

3. Will 2nd order upwind (CFX definition) will make the solution worst than even 1st order upwind scheme?





References:
[1]
Barth and Jespersen "The design and application of upwind schemes on unstructured meshes" .
Technical Report AIAA-89-0366, AIAA 27th Aerospace Sciences Meeting, Reno, Nevada, 1989.










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Old   May 22, 2011, 13:26
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Dear frends and specially ghorrocks any help and comments please ?
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Old   May 22, 2011, 20:01
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It has been a while since I looked into this stuff, but this is my understanding:

Quote:
Does it mean that the high resolution scheme of CFX and 2nd order upwind scheme of fluent are equivalent.
From your information they appear similar, if not the same. I was not aware the Fluent 2nd order upwind scheme had a limiter on it.

Quote:
Does it mean that the CFX 2nd order scheme is more like a baised 2nd order scheme with one term of upwind and 2nd term (anti diffusive term) is central differencing type?
There is no central differencing in the CFX high res scheme to my knowledge. Just first and second order upwinding.

Quote:
Will 2nd order upwind (CFX definition) will make the solution worst than even 1st order upwind scheme?
It should not. Where the extra dissipation of first order upwinding is required for stability the intention is this is detected and beta reduced to reduce the unstable 2nd order and increase the stable 1st order. But the user always has the option of selecting first order upwinding if it is not working.
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Old   May 23, 2011, 11:57
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It is written in CFX help that \nabla\phi\ is equal to the average of the adjacent nodal gradients. It clearly shows scheme is central differencing when \beta\ = 0.5
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Old   May 23, 2011, 19:08
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Quote:
It clearly shows scheme is central differencing when = 0.5
Not so clearly for me, I cannot find any comment to this effect. It says the CDS uses beta=1.0 and the del (phi) is now defined as the local element gradient.

So I cannot see anything which suggests beta=0.5 gives you CDS.
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Old   May 24, 2011, 04:14
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Quote:
It says the CDS uses beta=1.0
Does it mean that when we select specified blend factor option with beta = 1.0 , the scheme becomes CDS?
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Old   May 24, 2011, 07:37
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No, read the full sentence - the del (phi) is redefined in CDS, so the high res scheme cannot become the CDS as the del (phi) terms are different.
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Old   May 28, 2011, 21:24
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Quote:
Originally Posted by Far View Post
It is written in CFX help that \nabla\phi\ is equal to the average of the adjacent nodal gradients. It clearly shows scheme is central differencing when \beta\ = 0.5
No, it's not CDS! In the formula, \beta=0\ leads to 1st-order upwind, and \beta=1\ leads to 2nd-order upwind. \beta=0.5\ is a blend of 1st- and 2nd-order upwind schemes which supposedly is more accurate than 1st-order scheme, but also more stable than 2nd-order scheme. You should use \beta<1\ if and only if the 2nd-order upwind fails to converge.
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Old   May 31, 2011, 04:59
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What about high resolution scheme? since this scheme does not guarantee the 2nd order upwind scheme every where.
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Old   May 31, 2011, 08:21
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This thread is getting tiresome. Please read the documentation.

It clearly says that the CDS has a different implementation to the upwinding schemes so you won't be able to get the CDS from any version of upwinding schemes - first order, hybrid or high res.
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