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August 27, 2003, 15:39 
Node centered and cell centered.

#1 
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Hi,
Could someone tell me the difference between these two: Node centered and cell centered. I have looked in so many books and found it difficult to get a consistent meaning for these terms. Has anyone got a reference they consider excellent? Where are the points at which we calculate the values of interest in each case? Where is the control volume in relation to these points? How is the boundary condition treated. Thanks, Confused student! 

August 27, 2003, 18:24 
Re: Node centered and cell centered.

#2 
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As far as I know, dual cell approach is used for the CV in nodecentered method. For exmaple, in 2D triangle unstructured mesh, the dual mesh of delaunay triangulation can be defined by voronoi diagram.
I think Blazek's book is one of the easiest book to follow on this topic. Here's the link: http://www.cfdonline.com/Books/list...?author=Blazek%2C+J 

August 27, 2003, 18:29 
Re: Node centered and cell centered.

#3 
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If you need more info on delaunay triangulation and voroni diagram, check out the following web page: http://www.ics.uci.edu/~eppstein/gina/delaunay.html
Computational Geometry by Mark de Burg helped me a lot, although it doesn't discuss CFD at all. 

August 28, 2003, 04:41 
Re: Node centered and cell centered.

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Quite easy. In order to use a numerical solution method on your problem, you will need to build a mesh. A mesh consists of a set of points, which support cells. As usual, cells are not allowed to overlap and need to completely cover the computational domain.
Now that you've got a mesh, you need to define a field. For this purpose, you will choose a "location" in which the value will be defined. A cellcentred scheme stores the variable in all cell centres whereas a nodecentred scheme stores it in the points. There is also a bunch of other choices but I don't want to get into that now. 

August 28, 2003, 05:42 
Re: Node centered and cell centered.

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Hi,
Thanks. I use a code where the grid points (solution variables are stored at grid points) are located at the centre of a cell.The cell faces are midway between adjacent nodes. What type of code is this? 

August 28, 2003, 07:49 
Re: Node centered and cell centered.

#6 
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That's probably a finite volume method. The variables there are mean values of quantities in the cell (for example the density of a gas). In contrast, values on nodes usually represent the value of a function at the node, not a mean value (for example the pressure of the gas at exactly that point.


August 28, 2003, 10:39 
Re: Node centered and cell centered.

#7 
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Yes, it is a finite volume technique. All of the methods I have spoken of are finite volume techniques. I want to know how to define node centered and cell centered finite volume techniques. Where are the grid points in both cases, where is the computational cell (has it a grid point at its centre or at corners or midway along its faces..) where is the information stored. I want answers to these questions with regard to the cell and node centred techniques ina finite volume sense. Thanks for all of your help everyone.


August 28, 2003, 12:43 
Re: Node centered and cell centered.

#8 
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Wee, try this. When you build a mesh, you will have vertices but not cells on the boundary. If any of your computational points is actually ON the boundary, you are using a nodecentred FV technique; otherwise it is cellcentred.
Hope this helps to unconfuse you 

August 28, 2003, 14:39 
Re: Node centered and cell centered.

#9 
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Hi,
Thank you. When you say, "if any of your computational points is actually on the boundary", are you refering to the points at which, for example, we calculate the velocity? I assume if I create a mesh (the vertices)where the corners of the cell (in rectangular 3D mesh for example) are the vertices and I calculate the velocity at the centre of this cell, then I am using a node centred code? Would this be correct? Or is is also a requirement (in additon to the above) that I have a computational point on the boundary in order to be nodecentred? Thanks for the help guys. I am having a problem only with the naming strategy, the theory is fine. 

August 29, 2003, 13:54 
Re: Node centered and cell centered.

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Guys, Is it not true, that calculation is always done at nodes, i.e. in a node centered way. Then, how the solution is stored defines wether it is a node or cell centered code. In a node centered the solution is stored at the cell nodes themselves, and in a cell centered, the solution is averaged ( using the node values) to the cell center and then stored.....


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