Hi everybody,

I recently tried to find some references about FVM and especially those that detail the derivation of the discretization schemes for general geometries.

In the past I developed FVM numerical codes based on staggered grids and rectangular control volumes. Therefore, I feel like I know quite well the schemes derivation techniques for this special case.

But now I would like to find out how the FVM is generalized to non-rectangular geometries (with non-rectangular quad and triangular control volumes) and non-staggered grid (i.e. colocated grid). How are the flux evaluated at the cell faces ? Comparisons between staggered and colocated strategies (when both can be considered) ? ...

I already read the very well known book by Patankar and I recently purchased the book written by Versteeg and Malalasekera "An introduction to CFD : the Finite Volume Method". I was really disappointed since the latter (as the former) only deals with rectangular geometries and staggered grids.

Thus, could someone advice me concerning a good reference explaining clearly the complete derivation of FVM schemes for non rectangular geometries (and controle volumes) and colocated grid ?

Thanks in advance for your contribution

Anthony

Do you mean polygonal shaped control volumes (if not quad or triangular elements) ?

Look at the answer to a question regarding unstructured quad meshes (just search for "quad" in this forum). There I already gave a reference to a thesis for FV schemes on arbitrary grids.

(all for compressible flow !)

Frank

What about trying immersed-boundary method ?

what is immersed-boundary method please

A kind of somewhat recently developed method(?).

For simulation of complex/moving boundary problems using (fixed) Cartesian grids.

Kim.

Hi there,

Check out the the following article (ps format) I wrote with Dr. T.S. Lund, about Collocated Vs Staggered (To be submitted to J. Comp. Phys.) http://aero.uta.edu/~felten/resume/taicdl_art.ps

sincerely,

Frederic Felten.

Hello, all,

I would also like to know if there is any good book or thesis which describe the FVM clearly for incompressible flow with structured grid in a curvilinear coordinate system. i.e. a book which is similar as Versteeg's except that it is in curvilinear coordinates.

Regards

Li Yang

Hello, all,

I would also like to know if there is any good book or thesis which describe the FVM clearly for incompressible flow with structured grid in a curvilinear coordinate system. i.e. a book which is similar as Versteeg's except that it is in curvilinear coordinates.

Regards

Li Yang

Based on the theoratical results presented in hanbooks of numerical analysis, volume 7, Finite Volume Methods (the authors are Eymard, Gallouet and Herbin, 2001). I developed a Finite Volume Scheme for unstructured grid with constant interpolations functions (this is not CVFEM, nor FVEM, nor discountinous Galerkin).

If you are interested, I could give you a copy of a proceding, and If you can read french, a copy of my thesis.