# Cell-vertex and cell-centered finite volume method

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 September 6, 2003, 08:18 Cell-vertex and cell-centered finite volume method #1 Praveen Guest   Posts: n/a 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.

 September 7, 2003, 23:51 Re: Cell-vertex and cell-centered finite volume me #2 QKim Guest   Posts: n/a 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.

 September 8, 2003, 02:08 Re: Cell-vertex and cell-centered finite volume me #3 Praveen Guest   Posts: n/a 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.

 September 8, 2003, 22:30 Re: Cell-vertex and cell-centered finite volume me #4 QKim Guest   Posts: n/a 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.

 September 8, 2003, 23:58 Re: Cell-vertex and cell-centered finite volume me #5 Anthony Iannetti Guest   Posts: n/a 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