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9.3 Node ordering
For all mesh and post-processing file formats, the reference elements are defined as follows.
Line: Line3: Line4:
0----------1 --> u 0-----2----1 0----2----3----1
|
Triangle: Triangle6: Triangle9/10: Triangle12/15: v ^ 2 | | \ 2 2 2 9 8 |`\ |`\ | \ | \ | `\ | `\ 7 6 10 (14) 7 | `\ 5 `4 | \ | \ | `\ | `\ 8 (9) 5 11 (12) (13) 6 | `\ | `\ | \ | \ 0----------1 --> u 0-----3----1 0---3---4---1 0---3---4---5---1 |
Quadrangle: Quadrangle8: Quadrangle9:
v
^
|
3-----------2 3-----6-----2 3-----6-----2
| | | | | | |
| | | | | | |
| +---- | --> u 7 5 7 8 5
| | | | | |
| | | | | |
0-----------1 0-----4-----1 0-----4-----1
|
Tetrahedron: Tetrahedron10:
v
.
,/
/
2 2
,/|`\ ,/|`\
,/ | `\ ,/ | `\
,/ '. `\ ,6 '. `5
,/ | `\ ,/ 8 `\
,/ | `\ ,/ | `\
0-----------'.--------1 --> u 0--------4--'.--------1
`\. | ,/ `\. | ,/
`\. | ,/ `\. | ,9
`\. '. ,/ `7. '. ,/
`\. |/ `\. |/
`3 `3
`\.
` w
|
Hexahedron: Hexahedron20: Hexahedron27:
v
3----------2 3----13----2 3----13----2
|\ ^ |\ |\ |\ |\ |\
| \ | | \ | 15 | 14 |15 24 | 14
| \ | | \ 9 \ 11 \ 9 \ 20 11 \
| 7------+---6 | 7----19+---6 | 7----19+---6
| | +-- |-- | -> u | | | | |22 | 26 | 23|
0---+---\--1 | 0---+-8----1 | 0---+-8----1 |
\ | \ \ | \ 17 \ 18 \ 17 25 \ 18
\ | \ \ | 10 | 12| 10 | 21 12|
\| w \| \| \| \| \|
4----------5 4----16----5 4----16----5
|
Prism: Prism15: Prism18:
w
^
|
3 3 3
,/|`\ ,/|`\ ,/|`\
,/ | `\ 12 | 13 12 | 13
,/ | `\ ,/ | `\ ,/ | `\
4------+------5 4------14-----5 4------14-----5
| | | | 8 | | 8 |
| ,/|`\ | | | | | ,/|`\ |
| ,/ | `\ | | | | | 15 | 16 |
|,/ | `\| | | | |,/ | `\|
,| | `\ 10 | 11 10-----17-----11
,/ | 0 | `\ | 0 | | 0 |
u | ,/ `\ | v | ,/ `\ | | ,/ `\ |
| ,/ `\ | | ,6 `7 | | ,6 `7 |
|,/ `\| |,/ `\| |,/ `\|
1-------------2 1------9------2 1------9------2
|
Pyramid: Pyramid13: Pyramid14:
4 4 4
,/|\ ,/|\ ,/|\
,/ .'|\ ,/ .'|\ ,/ .'|\
,/ | | \ ,/ | | \ ,/ | | \
,/ .' | `. ,/ .' | `. ,/ .' | `.
,/ | '. \ ,7 | 12 \ ,7 | 12 \
,/ .' w | \ ,/ .' | \ ,/ .' | \
,/ | ^ | \ ,/ 9 | 11 ,/ 9 | 11
0----------.'--|-3 `. 0--------6-.'----3 `. 0--------6-.'----3 `.
`\ | | `\ \ `\ | `\ \ `\ | `\ \
`\ .' +----`\ - \ -> v `5 .' 10 \ `5 .' 13 10 \
`\ | `\ `\ \ `\ | `\ \ `\ | `\ \
`\.' `\ `\` `\.' `\` `\.' `\`
1----------------2 1--------8-------2 1--------8-------2
`\
u
|
The nodes of a curved element are numbered in the following order:
- – the element principal vertices;
- – the internal nodes for each edge;
- – the internal nodes for each face;
- – the volume internal nodes.
The numbering for face and volume internal nodes is recursive, ie. the numbering follows that of the nodes of an embedded face / volume. The higher order nodes are assumed to be equispaced on the element.