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numbering in unstructured grid

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Old   March 5, 2003, 04:07
Default numbering in unstructured grid
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reader
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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.

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Old   March 5, 2003, 05:11
Default Re: numbering in unstructured grid
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Madhukar M. Rao
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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
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Old   March 5, 2003, 08:26
Default Re: numbering in unstructured grid
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Praveen
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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
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Old   March 5, 2003, 10:05
Default Re: numbering in unstructured grid
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Nashat
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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, 123-135 (1988).

R. Löhner and M. Galle - Minimization of Indirect Addressing for Edge-Based Field Solvers; AIAA-02-0967 (2002).

R. Löhner - Applied CFD Techniques; J. Wiley & Sons (2001).

Regards,
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Old   March 5, 2003, 10:36
Default Re: numbering in unstructured grid
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Nashat
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Lohner, Rainald, "Renumbering strategies for unstructured-grid solvers operating on shared-memory, cache-based parallel machines", Computer methods in applied mechanics and engineering, Elsevier, Vol 163, pp.95-109, 1998
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Old   March 5, 2003, 11:36
Default Re: numbering in unstructured grid
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xueying
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I used GAMBIT to generate 10-node 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.
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Old   March 6, 2003, 03:23
Default Re: numbering in unstructured grid
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Rami
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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 k-th 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) }.
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Old   March 6, 2003, 14:14
Default Re: numbering in unstructured grid
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Abhijit Tilak
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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 un-ordered mesh. If you want to implement implicit/Semi-Implicit scheme your mesh (cells) must be re-ordered. 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
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Old   March 6, 2003, 14:58
Default Re: numbering in unstructured grid
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Nashat
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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+LU-SGS Method on Shared-Memory, Cache-Based Parallel Computers; AIAA-00-0927 (2000).

Sharov, D. and Nakahashi, K., "Reordering of Hybrid Unstructured Grids for Lower-Upper Symmetric Gauss-Seidel Computations," AIAA Journal, Vol. 36, No. 3, pp. 484-486, 1998.

Regards
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Old   December 31, 2010, 01:07
Default numbering in unstructured grid
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Quote:
Originally Posted by Nashat
;23498
Here are some references:

R. Löhner - Some Useful Data Structures for the Generation of Unstructured Grids; Comm.Appl.Num.Meth. 4, 123-135 (1988).

R. Löhner and M. Galle - Minimization of Indirect Addressing for Edge-Based Field Solvers; AIAA-02-0967 (2002).

R. Löhner - Applied CFD Techniques; J. Wiley & Sons (2001).

Regards,
Hi, I am new to CFD programming. Can anybody explain or send the tutorial on the bin renumbering for 3-Diemension, as Prof. Lohner discussed in Applied CFD Techniques.
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