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Old   February 20, 2002, 11:24
Default References for FVM
  #1
Anthony Wachs
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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
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Old   February 20, 2002, 11:36
Default Re: References for FVM
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frank
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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
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Old   February 20, 2002, 12:19
Default Re: References for FVM
  #3
Jongdae Kim
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What about trying immersed-boundary method ?
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Old   February 20, 2002, 12:49
Default Re: References for FVM
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ma
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what is immersed-boundary method please
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Old   February 20, 2002, 16:08
Default Re: References for FVM
  #5
Jongdae Kim
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A kind of somewhat recently developed method(?).

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

Kim.

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Old   February 20, 2002, 16:09
Default Re: References for FVM
  #6
Frederic Felten
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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.
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Old   February 20, 2002, 19:06
Default Re: References for FVM
  #7
Li Yang
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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

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Old   February 20, 2002, 19:09
Default Re: References for FVM
  #8
Li Yang
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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
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Old   February 20, 2002, 20:23
Default Re: References for FVM
  #9
Sebastien Perron
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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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