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March 5, 2003, 04:07 
numbering in unstructured grid

#1 
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Hi, when we use a usual structured grid (for example, rectangles in a 2D case), each node (or cell) receives its "natural" number. The unstructured grid looks as a chaotic set of nodes. How it is necessary to number its nodes and cells? Thank.
reader. 

March 5, 2003, 05:11 
Re: numbering in unstructured grid

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Unstructured meshes will, usually, not show any "natural" numbering pattern.
If you are writing a CFD solver for unstructured meshes, you will have to keep track of the neighbors for each cell, as well as its faces. Madhukar Rao ACRI 

March 5, 2003, 08:26 
Re: numbering in unstructured grid

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When you generate an unstructured grid, the grid generator will number the nodes somehow. You may want to renumber them for efficient cache utilization. See
R. Lohner: Applied CFD Techniques, Chapter 15 

March 5, 2003, 10:05 
Re: numbering in unstructured grid

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Here are some references:
R. Löhner  Some Useful Data Structures for the Generation of Unstructured Grids; Comm.Appl.Num.Meth. 4, 123135 (1988). R. Löhner and M. Galle  Minimization of Indirect Addressing for EdgeBased Field Solvers; AIAA020967 (2002). R. Löhner  Applied CFD Techniques; J. Wiley & Sons (2001). Regards, 

March 5, 2003, 10:36 
Re: numbering in unstructured grid

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Lohner, Rainald, "Renumbering strategies for unstructuredgrid solvers operating on sharedmemory, cachebased parallel machines", Computer methods in applied mechanics and engineering, Elsevier, Vol 163, pp.95109, 1998


March 5, 2003, 11:36 
Re: numbering in unstructured grid

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I used GAMBIT to generate 10node tetrahedral mesh. The node numbered well. Say, node 1,3,6,10 are always on the vertex, between 1 and 3 is always 2, between 1 and 6 is always 4, the others are the same.


March 6, 2003, 03:23 
Re: numbering in unstructured grid

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When you generate an unstructured grid, an additional piece of information is required to supplement the node coordinates and numbers, namely a connectivity table. This table lists the node numbers of each cell (or element). For example, in 2D, if the quadrilateral cell No. k comprises of the corner nodes numbered { n1, n2, n3, n4 }, the connectivity table has { n1, n2, n3, n4 } as its kth row (or coloumn).
For structured grid this information is redundant, since each cell indices are related to its node indices. For example, in 2D, cell (i+1/2,j+1/2) comprises of the nodes { (i,j), (i+1,j), (i,j+1), (i+1,j+1) }. 

March 6, 2003, 14:14 
Re: numbering in unstructured grid

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Hi,
The numbering of cells/nodes in unstructured grid goes beyond efficient memory utilization & reducing band width of the coefficient matrix. An fully explicit will work well with unordered mesh. If you want to implement implicit/SemiImplicit scheme your mesh (cells) must be reordered. If you don't do this the scheme reverts to explicit.... since updated value may not be available. The scheme is then at mercy of CFL condition. I was not aware of this until, I had to write a unstructured grid code for simulatin incompressible viscous flows. Intrestingly this is not stated in the literature that I came across. Probably it is implied or too "trivial" to be stated. Abhijit 

March 6, 2003, 14:58 
Re: numbering in unstructured grid

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Some more refernces which might be of interest:
D. Sharov, H. Luo, J.D. Baum and R. Löhner  Implementation of Untructured Grid GMRES+LUSGS Method on SharedMemory, CacheBased Parallel Computers; AIAA000927 (2000). Sharov, D. and Nakahashi, K., "Reordering of Hybrid Unstructured Grids for LowerUpper Symmetric GaussSeidel Computations," AIAA Journal, Vol. 36, No. 3, pp. 484486, 1998. Regards 

December 31, 2010, 01:07 
numbering in unstructured grid

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