Dear All,

Hi, my name is Apri. Currently, I am doing my thesis and it is about fluid. I would like to get some references (in .pdf files are really welcome) concerning "collocation grid" in finite volume method, i.e. how to use it to solve Navier Stokes.

I would be really grateful if I can get the information. Thank you in advance.

Sincerely,

Apri

I suppose you are referring to incompressible flow? Only in that case is collocated vs. staggered a really big issue.

Yes... I am dealing with incompressible flow.

Hate to sound like a professor, but:

Do you "colocation", with all variables located at nodes on a grid (opposed to staggered)?

or:

Do you mean "collocation", which is a method that is based (I think) on a particular superposition technique?

Just found this link (and a lot more) by Googling "Collocation", then "Differential Equations"

www.math.umn.edu/~pwkim/SymCol.pdf

Seems that, in principle, you could mean either one. But the codes would sure look different!

The first thing, all variables located at nodes of the grid, i.e. the opposite of staggered grid.

Hmmm... thanx, but this is not the one I want though. As far as I know, collocated grid is used in FEM and FDM. But it is also used for FVM, and this is what I am looking for (how to apply the collocated grid to FVM), since the treatment is different with staggered grid.

You could have a look at my Thesis (FVM on unstructured collocated grids), which is available on-line:

http://www.h.jasak.dial.pipex.com/

under Papers.

Enjoy,

Hrv

One of the earliest collocated methods for incompressible flow (at least that I know of) is the one by Rhie and Chow (AIAA Journal Vol 21 1983). May be a good starting point. There have been many other publications on this subject. As far as I understand, the staggered scheme is still the method of choice on structured grids. On unstructured grids it seems more complicated to construct a stable staggered scheme (although this has been attempted), so most collocated methods will probably be used for unstructured grids. A relatively recent survey of methods can be found in "Numerical methods for incompressible viscous flow", Advances in Water Resources, Vol 25, 2002 by Langtangen et al.

We have recently been looking into this subject and decided to go a somewhat different way: low-speed pre-conditioning of a compressible flow solver. Some collocated methods are essentially doing just that.

Folks, it's the spelling.

co_location is the deal with all variables located at nodes. Not staggered.

col_location is a mathematical technique for approximating functions, or interpolating, or some such.

They're different words.

Put colocation (one 'ell') and CFD into Google. At the bottom of the first page you start getting CFD applications.

Put collocation (two 'ell's) and mathematics into Google. You immediately get references to math professor's home pages, with talk of pseudo-spectral and spline approximations.

Look the article

T.Ye, R.Mittal, H.S.Udaykumar, and W.Shyy, An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries// J. of Computational Physics, v. 156, pp. 209-240, 1999.

This method looks like well known Kim & Moin fractional-step method. (Kim, J., Moin, P., Application of Fractional-Step Method to Incompressible Navier-Stokes Equations. // J.Comp.Phys. (59) 1985, pp. 308-323.)

But in this method all variables (including velocity) are stored in cell centers. I think it will be interesting for you.

Alexey.