Fiends: wouldl like to hear your views on use of staggered (vs. collocated) grids in LES

Hi, It's recommended to use staggered grids in LES if you have to resolve a problem with many variables.

May I ask why?

it's a physical requirement.

There is a very good exemple to explain that in:

An Introduction to Computational Fluid Dynamics: The Finite Volume Method

By: Versteeg, H.K. and Malalasekera, W. Addison-Wesley, 1996

There is another thread in this index on the same topic! I do not think staggered grids are better than colocated grids given both algorithms are stable! The problem with the colocated algorithm is that there is almost invariably pressure-velocity decoupling which is ofcourse to be expected. One can use the Rhie-Chow correction to remove this problem.

Once you have a stable colocated grid algorithm then I think it is more useful for complex geometries and also for geometries where there is lot of curvature where a simplistic use of Cartesian velocities will not work for the staggered grids.

regards, chidu...

You have touched on a number of points. I agree that a Rhie-Chow scheme (of whatever flavour) will prevent decoupling if implemented correctly. However, it also introduces a set of problems which are absent in a staggered scheme. Does it conserve mass? and, if so, are we happy with what a Rhie-Chow scheme labels mass?

Staggered grids with grid-orientated components perform relatively poorly for smooth flowfields and strong grid distortion. However, this is not the case for smoothly varying grids and, on balance, a staggered scheme is likely to be superior. True?

Do we want to perform predictions with strong grid distortions? For diffusion dominated problems the overwelming evidence (i.e. FE stress analysis) is yes it is a good way to cope with complex geometries. For complex convection dominated flowfields such as those encountered in LES there is no such evidence. True?

I do not have the book but would like to learn. Why is it a physical requirement for LES?

Hi andy,

The problem with staggered grids is not to do with grid distortion, but is to do with turning of the domain. Like a 90 degree bent in a pipe where Cartesian velocities defined at the cell face become ill defined. Therefore people use contravariant velocities along with staggered grids when extending it to geometries with bends.

Distorted grids are another story and should generally be avoided to maintain accuracy even with colocated grids.

About conservation of mass violation with the Rhie-Chow correction I am not very confident of making assertions. People also complain about the staggered grids that mass and momentum are not conserved in the same control volume. I think the key issue is weather the error is a discretization error or not (proportional to delta x). In other words, is the discretization "consistent" in the sense that errors reduce at a rate based on the grid spacing!

For simple geometries like a channel for example, staggered grids have been used with lot of success.

chidu...

I think we may be at cross purposes. I agree that staggered Cartesian components have limited use because they decouple when the staggering direction and the velocity component direction become misaligned. I was considering the use of grid orientated components. In the presence of strong local grid curvature (grid distortion) the terms transferring momentum between the grid components become large and so do their truncation error terms. This happens even if the flow is smooth leading to poor performance. However, if a curved flow and a curved grid are well aligned (e.g. a boundary layer over a smooth surface) the opposite occurs.

If the geometry is a complex and awkward shape how can you avoid distorted grids? If the scheme is boundary conforming it must work well in the presence of strong grid distortion. If the scheme is non-boundary conforming then the story is different but that shifts things back in favour of grid staggering. True?

I think consistency is a non-issue. It is hard to view it as anything other than a requirement for a sound scheme.

For RANS schemes the consequences of treating a mass flux as the interpolated "true" flux plus a smoothing component is rarely a problem in practice. However, for an LES scheme which aims to conserve other properties such as "energy" it may cause more serious problems. I believe this was part of the theme of Frederic's earlier posting. Can we confidently say that colocated are worse in this respect?

For LES is the balance really leaning towards colocated schemes? If not, why are they so popular?

Hi, I do not have any experience working with grid-oriented velocities. My hunch would be that it does involve more complicated coding effort; though I may be wrong on that. Also, the popularity of colocated grids for LES probably just follows from its popularity in general CFD. There might not be scientific reasons like "energy" conservation for that.

I am aware of efforts, say for example, at CTR in Stanford to create higher-order schemes which are both kinetic energy and momentum conserving in a discrete sense for the case of inviscid and incompressible flow also in the context of staggered grids.

In summary, I would not conclude that colocated grids have been proven to be better. Infact, I would be more confident about staggered grids.

regs, chidu...

you must look at this before,

An Introduction to Computational Fluid Dynamics: The Finite Volume Method

By: Versteeg, H.K. and Malalasekera, W. Addison-Wesley, 1996

hi everyone,

I think that a lot of questions asked concerning this topic (Grid in LES) could be answer just by reading this publication: Y. Morinishi, T.S. Lund, O.V. Vasilyev and P. Moin "Fully Conservative Higher Order Finite Difference Schemes for Incompressible flow". Journal of Comp. Phys.,Vol 143,pp 90-124, 1998.

It's a very good summary(& proof) for these schemes conservation properties. This publication also point out the problem of kinetic energy conservation for collocated grid.

Sincerely,

Frederic Felten. ps: contact me via email to get a copy of this article if you don't have any access to Journal of Comp. Phys.

Hi again,

An extension to this paper, (for non-uniform staggered grid) is the following publication:

"Higher Order Finite Difference Schemes on Non-uniform Meshes with good conservation Properties" Oleg V. Vasilyev, Journal of Comp. Phys., Vol 157, pp 746-761, 2000.

Sincerely,

Frederic Felten.