[emjay]

Hello Community,

i saw in a presentation from Mr. Jasak how he "bounded" the backward scheme with the

default   bounded backward;

code in fvSchemes.

my question is, what does the line does in the background?
how is the code

bounded

manipulating the "backward equation"

may be there is kind of a first order limiter implemented with a Euler diescretization or Crank-Nicholson method which blend the backward-scheme to bound the solution.

May somebody could show me the code snippet for bounded in ddt schemes.

best regards
eMJay

[clapointe]

Check out this thread (which refers to this link : https://openfoam.org/release/2-2-0/n...s-boundedness/) :

Meaning of 'bounded' keyword in fvSchemes.

Caelan

[cryabroad]

Maybe you guys know something that I don't. I understand what the bounded scheme does, and I myself have had experience of using bounded (which gives good results) and not using it (which crashes the simulation). So, I came to the conclusion that bounded is necesary for my case (transient, compressible, subsonic), but I do have the following question.

As emjay pointed out in the initial post, and before I dig deep into the source code, I thought that the bounded scheme works like a limiting function with a cutoff value on the variable itself or its time derivative. But from FOAM's explanation, it apparently only adds an additional term that is associated with continuity. This would suggest that if I have enough outer iterations within one time step, the effects of adding this term (and using Bounded) gradually decrease. But this is not the case, I simulated same case without Bounded, using different number of outer iterations, the simulation always crash. But with the Bounded scheme, if runs smoothly almost all the time. It seems to me that, by using Bounded (and thus adding the continuity associated term) the linear solver works far better. Why is it like this? This has to be something with the way the linear solver works I guess?

With the above question I have another rather small one. If the Bounded scheme works better for the linear solver, why don't we use it all the time? What is the cost of using it, does it slow down the calculation?

Thanks,
Ruiyan

[emjay]

Hello Ruiyan,

i think the mathematical correct description of this behaviour is consistency.

When the solution is not converged, the unbounded equation is not consistent with the bounded equation.

In the limit of convergence the result iterating to the same solution.
But with the unbounded equation small protuberances could gain instabilities.

i expect that for 1st order discretisation the additional numeric dissipation is dominant for damping the small errors.

But for a time and space accurate solution you need at least, 2nd order for the transient naiver stokes equation.

And there is no free lunch, if you are using the bounded keyword, you will spend a little bit more time for each iteration, but it could be that your simulation needs less iteration achieving convergence. (i didn't have testet this statement yet)

[cryabroad]

I agree, the small pertubations created by not using the bounded scheme grow larger and larger, which blow up the simulation. But what are the criteria though? I think this has something to do with the error propagation of a particular case.

I think you pointed out something that's interesting. I actually had such experience when doing unsteady RANS (uRANS). By using backward, the case tends to be very sensitive and easy to blow up, but by using Euler it proceeds smoothly. I think Euler is kind of a standard scheme in uRANS, at least it's commonly used in the literatures I've read. I need to learn more about error propagations man (those are not easy).

[emjay]

Generally a higher order integration in time and space is less diffusive and also less stable.
Euer is the simplest way to do (in OpenFOAM implicit Euler), but the time accuracy is only 1st order, which is very diffusive.
For accurate time integration there (in OpenFOAM) exist two 2nd order schemes:
1) backward (2step Adam Bashforth Method )
2) CrankNicolson

Some Information about that topic could you find in the Phd Thesis from Hrvoje Jasak

[cryabroad]

I'm more familiar with spatial errors than temporal ones, I think it's time to pick those up. I'm doing LES now so they are becoming more and more important to me. I'll dig deep into Prof. Jasak's thesis to find out more!