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reader March 5, 2003 04:07

numbering in unstructured grid
 
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.

Madhukar M. Rao March 5, 2003 05:11

Re: numbering in unstructured grid
 
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

Praveen March 5, 2003 08:26

Re: numbering in unstructured grid
 
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

Nashat March 5, 2003 10:05

Re: numbering in unstructured grid
 
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,

Nashat March 5, 2003 10:36

Re: numbering in unstructured grid
 
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

xueying March 5, 2003 11:36

Re: numbering in unstructured grid
 
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.

Rami March 6, 2003 03:23

Re: numbering in unstructured grid
 
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) }.

Abhijit Tilak March 6, 2003 14:14

Re: numbering in unstructured grid
 
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

Nashat March 6, 2003 14:58

Re: numbering in unstructured grid
 
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

CFD_naive December 31, 2010 01:07

numbering in unstructured grid
 
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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