I am wondering...

Why do people still bother with staggered grids? We know they are not suitable for unstructured grids ie. automatic meshing etc. etc....

I believe the time has come to grow up and use co-located meshes. Industry have little or no application for staggered grid CFD. Imagine modelling a complex valve using staggered grid (good luck)

Comments are welcome

(1). I think, the multi-block, structured mesh is the optimum combination in dealing with complex problems. (2). The reason is, the flow does not treat the complex geometry as random geometry. So, one can always study the local flows and global flows to come up with the right combination of mesh zones. (3). For unstructured mesh to work, it must be adaptive. Otherwise, the unstructured mesh becomes a random mesh (it follow the mesh generation geometric rule, rather than the flow field solution). (4). co-located vs staggered mesh is mainly related to the historic development of the Imperial College method of incompressible flow , primitive variable formulation. I don't think, one must use a particular formulation. (5). If the solution is good and if you like it, then it doesn't matter how you solve the problem. (there are resons why the staggered mesh was used, I think. ) (6). Anyway, I don't use either method in my codes.

If you do not use co-located or staggered arrangement in you codes as mentioned, you must be doing something really good. Can we have your paper (or papers) please?

I say,

John, are you using a finite volume or a finite element aproach? If finite volume...I'll be VERY interested in your meshing approach if not Co-locatet or staggered.

Regards Barry

My other point John is that co-located meshes may be used effectively for structured block meshing. Why do we then still resort to staggered meshing?

I think is boils down to pressure velocity coupling, Staggered meshing were so to say "invented" to cope with the checkerboard pressure fields in the solution. But I think the problems with co-located are resolved to a great extend by the so called Rhie & Chow interpolation scheme.

Any comments on this?

Compare the stability of buoyant flow solutions on both staggered and non-staggered arrangements. The former is vastly superior.

I agree with Fred's comment, which also applies for other problems involving large variations in body forces. A well-known problem area is flow through resistive media with resistance discontinuities, as say experienced on entry and exit to a porous block. Great care is needed with co-located schemes for such problems, otherwise the result is convergence problems and/or non-physical solutions. Some codes use special practices which modify the Rhie-Chow scheme to improve convergence and accuracy.

hi there,

well the debate between colocated and staggered is really at stake when ones want to simulate curvilinear meshes. In cartesian geometries, the staggered layout is the obvious choice. Now for curvilinear meshes, the bookeeping and the transformation associated with a staggered arrangement is horrible. That's why the colocated has been most of the time employed. Now a lot of misconception regarding these two arrangement has circulating. For those of you interested in incompressible LES, DNS. please take a look at the abstract(6 pages) that i wrote with Dr. T.S. Lund and that we'll be presented at the Third international AFSOR conference this august 2001. To download this paper click the link: http://math.uta.edu/~taicdl/paper/regular/felton_13.pdf

If you have any comments, please let me know.

sincerely,

Frederic Felten.

Mr Barry, if you are interested in not using a staggered grid nor a co-located grid with "classical" finite volumes, I could have something for you.

For my PHD thesis I use an unstructered 3D mesh and the same grid for both the pressure and the velocity field. The false pressure modes are avoided with a re-interpolation of the velocity on the cell interfaces before proceeding with the projection. This re-interpolation is different from the rhie-chow approach. I could send you a copy of a conference that I will give in a few weeks. The results have not been published yet.

Hello Seb,

I would be interested in reading about your approach. Would it be possible to get a copy also?

Thanks,

Jeff

Hi, Barry

So someone out there is still bothered with staggered v/s non-staggered! Each one has it's own advantages/disadvantages. some of my observations are below (from my experience) 1. Staggered grid gives excellent convergence of P' equation. Non-Staggered Grid convergence is not good unless u use PCCG /ILU (SIP) procedure. 2. Staggered grid is good in handling situations where velocity equations are coupled with other equations, I mean buoyant flows. 3.Staggered Grid on BFC' (curvilinear coords)s is ugly to implement! 4.Staggered Grid is not preferred for doing LES/DNS computations (because of voilation of certain conserved quantities) 5. Rhie Chow procedure for preventing p-v decoupling is ugly it gives relaxation parameter dependence.(although it has been rectified! by Mujumdar & Rodi)

Hope this helps Abhijit Tilak

(1). If the p-field can be decoupled from the momentum equation based on incompressible flow theory, then we know that there is no need to have worry about it all the time. (2). In theory, P, u,v, etc must be point value, and must be defined at the same point. That is also the fundamental theory in thermodynamics. (3). So, it is all right to have v-field defined on one grid. And the solution would contain some numerical errors (approximation solutions). (4). If one use the same v-field and try to deduce the corresponding p-field on the same grid, then you will get (v-field error + integration error) for the p-field. This is fine, because one would stop at the p-field integration. (5). If this p-field with two kind of errors is then feed into the momentum equation, then it will act as the source term for the momentum equation for the new v-field. Let's stop at this point for a moment. (6). If we don't want to change the old v-field, that is, to keep the new v-field the same as the old v-field, then the p-field solution must be changed. (7). And the one way to change this is to absorb the integration error in a different system, thus you have staggered system. (8). The staggered system will provide flexibility to absorb the error in its own grid system. Thus provide a compatible solutions at the momentum equation level. In other words, v-field and p-field must satisfy the momentum equation, but they are defined on separate grid systems. And each will be good solution in their own grid system. (9). If you eliminate this flexible connection, then the system is over-specified, because v-field alone can be determined separately without any knowledge of the p-field, based on the incompressible flow theory. (the only way to get two related variables exactly is to have both solution exact, which is not possible in CFD approximation). (10). So, the pressure-based approach to incompressible flows is to re-distribute the error to v-field, and p-field, such that they will satisfy the momentum equation in some fashion. It is hard because, in some cases, there will be large error in the v-field because of the mesh distribution. In this case, p-field will have to absorb the extra errors which can be hard to take when pushing the convergence for both v-field and p-field at the same time.

(1). In your Figure.1, if I plot the centerline U+ against the mesh size fo three cases (A, B and C), the mesh independent solution is not reached at the C-case with (64x64x32) mesh. (2). Using my hand extrapolation and my eyeball judgement, at the mesh size of (128x128x32), the centerline U+ will dip below U+=19 value. And thus make the comparison between the case-C and DNS premature. (3). In other words, using your data and my extrapolation, the result from (128x128x32) case would produce noticeable underprediction relative to the DNS result of centerline velocity U+. (4). If my prediction is correct, then both methods would produce poor solutions at (128x128x32) mesh resolution. And even at (128x128x32) I think, the solution obtained is still changing with mesh size. (5). My suggestion is: Find out whether fine mesh solution of (128x128x32) is consistent with my prediction. That is, the solution would produce visible under-prediction of the centerline velocity U+.

dear john,

That is true that case C (64*64*32) is not sufficient for comparison with DNS. A finer mesh for example like you suggested 128*128*32 could be employed and both the staggered and the collocated should be extremely close to the DNS solution (staggered and collocated right on top of each other). Now the purpose of this paper is not to show that both schemes are performing really well at high mesh resolution, but to show which one is more accurate regarding the conservations errors associated with each schemes. For my defense, it's also important to notice that this is the "abstract" and not the final paper. Nevertheless ido appreciate your suggestion and comments. Hence the final paper is completed i could send you a copy if you are interested.

Sincerely,

Frederic Felten.

(1). Thank your for the paper ahead of the time. (2). My comment is just a comment.