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 Anthony Wachs February 20, 2002 11:24

References for FVM

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 ?

Anthony

 frank February 20, 2002 11:36

Re: References for FVM

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

 Jongdae Kim February 20, 2002 12:19

Re: References for FVM

What about trying immersed-boundary method ?

 ma February 20, 2002 12:49

Re: References for FVM

 Jongdae Kim February 20, 2002 16:08

Re: References for FVM

A kind of somewhat recently developed method(?).

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

Kim.

 Frederic Felten February 20, 2002 16:09

Re: References for FVM

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.

 Li Yang February 20, 2002 19:06

Re: References for FVM

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

 Li Yang February 20, 2002 19:09

Re: References for FVM

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

 Sebastien Perron February 20, 2002 20:23

Re: References for FVM

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.

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