Central DIfference
 

Hi,

I am trying to incorporate Central Difference scheme, for convetion terms in my code, as I am aware from the Literature that it is very unstable, so I tried to use the deferred correction technique(for convection terms only) that was mentioned in the Ferzier, Peric's book, and code which was blowing before began to run normally...

But the problem I am facing is that, for the Backward facing step, I am not able to see the circulation bubble, behind the step, and all the vectors seem to be directed only in one direction and not in the other direction, (that is there is no negative velocity)

Any help in this regard will be highy appreciated!!

Thanks in advance,

Glen.

Re: Central DIfference
 

I use a central difference scheme and it blows if i treat the convective term as d(uiuj)/dxj (divergence form). However, if i treat it as uj d(ui)/dxj (convective form) it is stable. Do you use the convective form? If not you might want to try it. I am able to capture the circulation bubble for the backward facing step.

Re: Central DIfference
 

You can use upwinding schemes based on CBC approach. For this see paper by VG Ferreira et al. in International Journal for Numerical Methods in Fluids, 2002.

By Valdemir

Re: Central DIfference
 

Dear Ferreira,

I got hold of the paper that you had quoted, but it had all the different ways of discretizing the convection terms, also mentioned are the things that CD and QUICK schemes fail in their cases, and the reson for it,which is very good.

But I am looking for a way to stabilise, my code by using CD for convection terms, as my goal is to intoduce LES once my CD starts to work fine. I have also seen another paper by the same author titled 'Direct testing of subgrid scale models in large-eddy simulation of a non-isothermal turbulent jet', where in a 6th order compact scheme, has been applied for convection terms.

I would be happy, if you can provide me with some info to stabilise my code, and moreover I am using finite volume technique, with a staggered grid.

Thanks,

Glen.

Re: Central DIfference
 

Your problem may not be linked with CD: try Upwinding and see if the right result is obtained.

Re: Central DIfference
 

HI John Luo,

Thanks for replying, I am afraid my code works well for Upwind and also Hybrid schemes, but I face the problem only when I switch over to central diff for convection terms, I checked my coding for Central difference, I looks fine, but as there is a limited visc(due to the model itself), I think I need to add some artificial damping in that case. If you have any experience in that kindly advice.

Thanks in advance,

Glen

Re: Central DIfference
 

Hi Glen

what sort of Peclet number is present in your simulation. The hybrid scheme switches to upwind as long as Peclet number is grater than 2. That means the CD scheme goes unstable when Pe >= 2. To avoid this and not to introduce additional artificial viscosity, which is your case as you intend to do LES, you could refine your computational grid and see if it helps.

Re: Central DIfference
 

Hi Vladimir,

Thanks for replying, I have tried what you have stated above, and it goes like, I need to refine the grid beyond the computational capabilities, and this may not be possible if, I am going to use high Re, I have read many LES papers where in high reynolds number flows have been simulated using central difference, although the way how the problem of treating convection term centrally to circumvent this problem(less diffusion) has not been mentioned!!!!

Thanks,

Glen

Re: Central DIfference
 

read what fluent manual says:

26.2.7 Bounded Central Differencing Scheme

The central differencing scheme described in Section 26.2.6 is an ideal choice for LES in view of its meritoriously low numerical diffusion. However, it often leads to unphysical oscillations in the solution fields. In LES, the situation is exacerbated by usually very low subgrid-scale turbulent diffusivity. The bounded central differencing scheme is essentially based on the normalized variable diagram (NVD) approach [ 189] together with convection boundedness criterion (CBC). The bounded central differencing scheme is a composite NVD-scheme that consists of a pure central differencing, a blended scheme of the central differencing and the second-order upwind scheme, and the first-order upwind scheme. It should be noted that the first-order scheme is used only when the CBC is violated.

NOTE: the Section 26.2.6: mentions the CDS same as perics book, that is

phi_f = implicit_upwind_oart + explicitpart( phi_cds - phi_up)

hope this gives some hint.

Re: Central DIfference
 

Hi Zxaar,

Thanks for replying, I trid my luck with the deffered correction approach, as stated by you and also given in Ferziger and Peric's book, I have a small doubt regarding it...

I also use the staggered grid system as mentioned in the book, so for the U-control volume, as per the deffered approach, we have to use the velocities from the previous iteration to be multiplied by the mass flux (which is a difference of UDS and CDS), so for the East and the West face, I will use the U-velocity, whereas for the North and South face should I use the U-velocity (for the U-Control volume) or use the V- velocity.

And the vice versa applies for the V-contol volume in 2-D, moreover will it matter much If use deffered correction approach only for convetive terms and neglect the diffusive terms.

Thanks,

Glen.