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-   -   Cell-vertex and cell-centered finite volume method (https://www.cfd-online.com/Forums/main/6537-cell-vertex-cell-centered-finite-volume-method.html)

 Praveen September 6, 2003 08:18

Cell-vertex and cell-centered finite volume method

If you have a triangular unstructured grid with Nv vertices and Nt triangles then Nv:Nt = 1:2 approximately. With a cell-vertex scheme the unknowns are stored at the vertices and with cell-centered they are stored at cell centres. So there are twice the number of degrees of freedom with cell-centered than in cell-vertex scheme. So how come both methods will give roughly the same accuracy on a grid which is more or less uniform (ie not highly anisotropic. In this case the accuracy of cell-centered scheme degrades.). Any references on this would be appreciated.

 QKim September 7, 2003 23:51

Re: Cell-vertex and cell-centered finite volume me

Praveen:

I'm also very interested in reading more on this issue. The 1:2 ratio is right, but, I'm wondering if they give the (more or less) same accuracy. One of Dr. Venkatakrishnan's ICASE reports discusses the accuracy associated with CC and CV method. I think the report points out that the volume (area) of a cell in CC method is generally smaller than the cell area in CV method. The ICASE report cited an AIAA paper by Dr. Frink. I will post the more details if you need them.

The number of flux computations required per a control volume is generally larger in CV method than in CC method. On the other hand, the ratio between the number of cells is 1:2 as you pointed out. So, as for the cost (excluding memory), I'm not sure that CC method is much more expensive than CV method as I had been thinking.

 Praveen September 8, 2003 02:08

Re: Cell-vertex and cell-centered finite volume me

I would like more details/references, thank you. I feel that the accuracy is determined by the accuracy of the flux integral. And the number of flux computations is same in CC and CV (assuming a centered-dual cell in CV). There are less number of faces per/cell in CC but more cells while there are more faces per/cell in CV but less number of cells. The number of flux evaluations which is equal to the number of edges is the same in both.

 QKim September 8, 2003 22:30

Re: Cell-vertex and cell-centered finite volume me

Here's the link to the report by Dr. Venkatakrishnan:

http://techreports.larc.nasa.gov/ica...ase-1995-3.pdf

AIAA paper 93-3500 by Dr. Frink, Dr. Pirzadeh and others.

If you find more references, would you post them? Thanks.

 Anthony Iannetti September 8, 2003 23:58

Re: Cell-vertex and cell-centered finite volume me

Dimitri Mavriplis of ICASE, now at ?, wrote a lot of NASA Langley / ICASE Papers comparing the two methods. I think it is a memory versus computation issue. I forget the specifics. I work with CC codes. For a variety of cell types, CC COULD be easier, because the dual mesh is a little abstract for quad, hexm, etc.. (non simplical) meshes.

Tony

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