Mesh node ordering

Overview

The node ordering followed by Kratos is the very same considered by the pre/post-processor GiD. You can see the notation considered by them here.

Node ordering

Following the documentation structure used in GMSH we represent the node ordering considered in Kratos.

Additionally everything related with geometry implementation can be directly consulted on the geometries code.

Line

Line2D2/                   Line2D3/                   Line2D4/                   Line2D5/   
Line3D2:                   Line3D3:                   Line3D4:                   Line3D5:   
                                                
0----------1 --> u      0-----2-----1               0---2---3---1              0--2--3--4--1

Triangle

Triangle2D3/               Triangle2D6/               Triangle2D10/               Triangle2D15/     
Triangle3D3:               Triangle3D6:               Triangle3D10:               Triangle3D15:     

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
             

Quadrilateral

Quadrilateral2D4/      Quadrilateral2D8/       Quadrilateral2D9/
Quadrilateral3D4:      Quadrilateral3D8:       Quadrilateral3D9:

      v
      ^
      |
3-----------2          3-----6-----2           3-----6-----2 
|     |     |          |           |           |           | 
|     |     |          |           |           |           | 
|     +---- | --> u    7           5           7     8     5 
|           |          |           |           |           | 
|           |          |           |           |           | 
0-----------1          0-----4-----1           0-----4-----1 

Tetrahedra

Tetrahedra3D4:                          Tetrahedra3D10:

                   v
                 .
               ,/
              /
           2                                     3                              
         ,/|`\                                 ,/|`\                          
       ,/  |  `\                             ,/  |  `\       
     ,/    '.   `\                         ,7    '.   `9     
   ,/       |     `\                     ,/       8     `\   
 ,/         |       `\                 ,/         |       `\ 
0-----------'.--------1 --> u         0--------6--'.--------2
 `\.         |      ,/                 `\.         |      ,/ 
    `\.      |    ,/                      `\.      |    ,5   
       `\.   '. ,/                           `4.   '. ,/     
          `\. |/                                `\. |/       
             `3                                    `1        
                `\.
                   ` w

Hexahedron

Hexahedron3D8:         Hexahedron3D20:       Hexahedron3D27:

       v
3----------2            3----10----2           3----10----2     
|\     ^   |\           |\         |\          |\         |\    
| \    |   | \          | 15       | 14        |15    23  | 14  
|  \   |   |  \         9  \       11 \        9  \ 20   11  \  
|   7------+---6        |   7----18+---6       |   7----18+---6 
|   |  +-- |-- | -> u   |   |      |   |       |22 |  26  | 24| 
0---+---\--1   |        0---+-8----1   |       0---+-8----1   | 
 \  |    \  \  |         \  17      \  19       \ 17    25 \  19
  \ |     \  \ |         12 |        13|        12 |  21    13| 
   \|      w  \|           \|         \|          \|         \| 
    4----------5            4----16----5           4----16----5 

Prism

Prism3D6:                      Prism3D15:              

           w
           ^
           |
           3                       3                          
         ,/|`\                   ,/|`\                    
       ,/  |  `\               12  |  14               
     ,/    |    `\           ,/    |    `\          
    4------+------5         4------13-----5       
    |      |      |         |      9      |        
    |    ,/|`\    |         |      |      |        
    |  ,/  |  `\  |         |      |      |       
    |,/    |    `\|         |      |      |       
   ,|      |      |\        10     |      11       
 ,/ |      0      | `\      |      0      |        
u   |    ,/ `\    |    v    |    ,/ `\    |       
    |  ,/     `\  |         |  ,6     `8  |        
    |,/         `\|         |,/         `\|       
    1-------------2         1------7------2        

Pyramid

Pyramid3D5:                        Pyramid3D13:


               4                                 4
             ,/|\                              ,/|\
           ,/ .'|\                           ,/ .'|\
         ,/   | | \                        ,/   | | \
       ,/    .' | `.                     ,/    .' | `.
     ,/      |  '.  \                  ,9      |  12  \
   ,/       .' w |   \               ,/       .'   |   \
 ,/         |  ^ |    \            ,/         10   |    11
0----------.'--|-3    `.          0--------8-.'----3    `.
 `\        |   |  `\    \          `\        |      `\    \
   `\     .'   +----`\ - \ -> v      `5     .'         7   \
     `\   |    `\     `\  \            `\   |           `\  \
       `\.'      `\     `\`              `\.'             `\`
          1----------------2               1--------6-------2
                    `\
                       u