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Discretization of transient terms in steady state

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Old   November 4, 2021, 11:07
Default Discretization of transient terms in steady state
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Hi,

I know that CFX uses a pseudo-transient approach to reach a steady state solution. However, I could not find any information in the solver-theory manual or in this forum if CFX uses a 1st or 2nd order backward euler scheme to discretize the transient terms. Maybe I'm missing something but does anybody know where I could find this information?

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Old   November 4, 2021, 12:29
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Your question confused two things:

Pseudo transient discretization vs True transient discretization

transient discretization order methods have no relevance in the pseudo-transient approach since the solution should be independent of how it got there.

I think you are asking for something else. Let us see what that really is.
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Old   November 4, 2021, 13:48
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Thanks for the quick response!

Please correct me if I'm wrong in the following. The set of governing equations is discretized in time even for steady calculations in CFX with a "false" time step. So time proceeds until a steady state solution is obtained. In order to solve the transient term in the discretized equations I need a scheme or method to do it. In the theory guide two are presented namely 1st and 2nd order backward euler. And that's where my questions aims at. I want to know which scheme CFX uses for the steady state case.

The Fluent theory guide explains everything pretty clearly, but I want to know how it is done in CFX.
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Old   November 4, 2021, 14:17
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It may look for some like 1st order discretization, but it is not.

If you thought from the Fluent theory that is a transient scheme, then the answer you want is: "the same as shown in the Fluent theory"

Nothing different.
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Old   November 4, 2021, 14:34
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So what is it then? Is there any paper/book/manual or something which describes properly what CFX does?

Last edited by LuckyGuy; November 4, 2021 at 16:03.
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Old   November 4, 2021, 16:30
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Exactly as described in the Fluent theory page
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Old   November 5, 2021, 03:11
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I missed things up yesterday and got confused, but I think now it's clear to me.

So, CFX uses a implicit pseudo-transient under relaxation (see Fluent Theory Chap. 24.6 "Pseudo Transient Under-Relaxation", Eq. 24.99) to march to the steady state solution. Is there a general formula to describe this and how are the coefficients calculated in this equation?
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Old   November 5, 2021, 03:37
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The coefficients are the linearisation of the non-linear terms in the Navier Stokes equations. They are updated each coefficient loop. This is also in the Fluent Theory manual, section 24.2 (especially 24.2.1).
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Old   November 5, 2021, 04:13
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Now everything is clear. Didn't know CFX and Fluent use the same method, that's what got me confused, I guess. Thanks for helping me!
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Old   November 5, 2021, 05:12
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A key reason Fluent and CFX came together under the ANSYS company was so they could share key bits of their respective technologies. Fluent did not originally have the coupled solver.
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