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ZY Sun September 8, 2000 22:48

Projection methods
Dear all,

I am working in Large-Eddy Simulation(LES) and programming a new 3d LES code with the finite-volume (FV) method on a structured grid.

So far, most of the LES code use Projection method (Peyret, R. and Taylor, T.D.) on a staggered grid, some researchers use SIMPLE family methods with Rhie-Chow method to deal with zig-zag pressure oscillatory as well.

In my work, I want to use projection methods, and I think that I also need use Rhie-Chow techniques as similar to used in SIMPLE methods.

Now, I met a problem that the solution of pressure is not convergent.

I hope anybody who has experience in using Projection method with FV methods on a structure grid gives me some ideas.

many thanks

yours zy

Tareq Al-shaalan September 9, 2000 00:47

Re: Projection methods
Have you checked your global mass conservation? This has to be zsero to the mchine acurecy for the pressure equation to converge.

After how many itrations or time steps strat to divarge?

Tareq Al-shaalan

ZY Sun September 9, 2000 11:14

Re: Projection methods
I guess the problem exists in the process of the pressure evaluation.

For the prodictor step: explicit time marching method is adpoted, low-storage 3-order Runge-Kutta in this code.

The projection method is used in the calculating pressure as a corrector step.

In the corrector step, at the beginning, say first and second iterating step, global mass conservation is OK. The residual, difference of right- and left-had side of pressure equation, is some 200. And then the residual keeps going up with iterative step, the global mass conservation gradually loses as well.



Tareq Al-shaalan September 10, 2000 00:33

Re: Projection methods
If you are specifying velocities at the boundaries, The sum of the right hand side has to be exactly zero ( to the machine accuracy). Also the sum of the all column in the left hand side of the matrix has to be zero

A*P = R

First check that

SUM(R) = 0 SUM(each column in A) = 0


Then adjust for the singularity in the matrix A by specifying a pressure at one nodal point.

frederic felten September 11, 2000 17:20

Re: Projection methods
hi there,

I guess that by projection methods, you're actually solving a poisson equation for the pressure equation. Well with staggered grid, it should be pretty straight forward. Just take a look at the following publication: Morinishi Y., Lund T.S. et al. Journal of computational Physics, Vol 143, pp 90-124, 1998.

You can download this article at

Dr Lund web page also have a link (bottow of the page) to a staggered isotropic turbulence code, using FVM in 3D, with fractional step method, projection step(poisson equation), DNS and LES. Check the file after you have downloaded the archive file.

If you have any problem, just let me know, i'm one of Dr Lund Ph.D students.


Frederic Felten

ZY Sun September 11, 2000 20:35

Re: Projection methods
Hi, Frederic,

I am a PhD student as well, I know the staggered grid. In our department, there are some LES codes on staggered grid. My job is developing a new 3d LES code with non-staggered gird, for engineering application, and then compare the results from the new LES code with some old ones on staggered grids.

Last month, I just finished programming a new LES code with SIMPLE family methods as a solution of pressure, but I found some disadvantages of SIMPLE method used in the region, such as Pelect number problem etc.. So I intend to develop another LES code with projection methods usually used in present most of the LES codes. After literatures collecting, I failed in finding any references regarding projection on a non-staggered grid.

In my opinion, the LES code with staggered grid is good at fundamental research. For non-staggered grid, compared with staggered grid, it is more suitable for practical application (this is a big issue). So far, the LES has been developed for over ten years. With Chie-Chow techniques, it is easy to deal with pressure oscillatory on a non-staggered grid. I 100% believe that someone have/had tried this way in past over ten years. I want to know why until today reports regarding hardly have been seen. Maybe this way no exit?

Anyway, I will visit the address you recommended. I had read Dr. Lund's papers.

Yours Banny

Joel Cambo September 12, 2000 11:51

Re: Projection methods
Why dont you check with Kim or Moin's group. They have used projection methods for DNS and LES for years.

ZY Sun September 12, 2000 13:02

Re: Projection methods
Yes, I had checked their group(CTR). I checked all of their papers, reports, and briefs posted on the net. However, I could not find any information regarding the projection methods with a non-staggered grid.

I have a feeling, so far LES has obtained a development with the value of pratical application over 10 years. But up to today, the staggered grid sounds still ``mean-stream''. Some ``non mean-stream'', let's call them branches, have been found, such as unstructured grid, structured grid (non-staggered grid), and SIMPLE family methods with respect to projection method, etc..

I hope to obtain some experience from anybody who has/had researched in the region projection method on a nonstaggered grid, particularly using co-located mesh.

kalyan September 12, 2000 14:13

Re: Projection methods
LES community has some how stayed away from non-staggered grid methods. The probable reason is the fact that the pressure-velocity coupling required special attention and LES community seems to prefer simplicity in the code. It appears that most LES researchers would much rather deal with filtering concepts and/or turbulence rather than be code developers. In problems like backward facing step which has more or less become a benchmark for LES codes, the issue of pressure at the corner is still not fully resolved. In staggered grid codes, there is no pressure variable defined at the corner and the pressure at the corner is a non-issue (although some people have argued on this very forum that by using a staggered mesh at the corners and avoiding a pressure variable at the corner is equivalent to solving a problem with a smoothed-out corner). Nevertheless, the LES codes produce reasonable accurate recirculation zones for this problem.

I do however agree that a non-staggered codes is preferrable for practical problems. The pressure-velocity coupling and the wall pressure BC seem to the issues that one needs to pay most attention to. There have been some developments in this direction by Prof. Street's group at Stanford (search for "Yan Zang" and "fractional step" on JCP website, around 1994-1995 time frame), Prof Mittal's group (at UF, Gainesville). The two methods are quite similar. One group uses curvilinear grids while the other deals with complex boundaries (quite successfully) on a cartesian grid.

There are also LES methods based on semi-staggered grid layouts by researcher like Prof. Ragab (Virginia Tech or VPI, I forget which one) and Prof. Golub (Stanford).

Hope this helps.


frederic felten September 15, 2000 18:00

Re: Projection methods
hi ZY sun,

If you're looking for a paper that compares staggered and collocated in curvlinear coordinates for turbulent flows?? Well take a look at this following reference (It took me a some efforts to find it):

"High-Order Finite-Difference Method for Incompressible Flows Usibg Collocated Grid System." T. Kajishima, T. Ohta, K. Okazaki and Y. Miyake JSME International Journal, Series B, Vol 41, N 4, 1998


Frederic Felten.

PS: tell me if that's what you were looking for!

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