# TET_MESH_ORDER20 Cubic Tet Mesh Definition

TET_MESH_ORDER20 is a data directory which contains examples of 20-node "tet meshes" (meshes of tetrahedrons). In such a mesh, the fundamental shape is a tetrahedron, but each tetrahedron is described by 20 nodes, namely, the four vertices, and 12 midside nodes, and 4 mid face nodes.

The definition of an order 10 tet mesh requires two files:

• the node file lists the coordinates of a set of points.
• the element file lists groups of 20 node indices, which form each element.

There is little agreement about how to order the nodes that describe a 20-node tetrahedron. The first four nodes are always the vertices.

Assuming the vertices are A, B, C and D, Gmsh uses the following ordering:

```    1:    a
2:        b
3:            c
4:                d
5: (2*a  +b        )/3
6: (  a+2*b        )/3
7: (    2*b+  c    )/3
8: (      b+2*c    )/3
9: (  a    +2*c    )/3
10: (2*a    +  c    )/3
11: (2*a        +  d)/3
12: (  a        +2*d)/3
13: (     b     +2*d)/3
14: (   2*b     +  d)/3
15: (       +  c+2*d)/3
16: (       +2*c+  d)/3
17: (  a+  b+  c    )/3
18: (  a+  b    +  d)/3
19: (      b+  c+  d)/3
20: (  a+      c+  d)/3
```

Leo Rebholz used the following ordering:

```    1:    a
2:        b
3:            c
4:                d
5: (2*a  +b        )/3
6: (2*a    +  c    )/3
7: (  a+2*b        )/3
8: (  a    +2*c    )/3
9: (  a+  b+  c    )/3
10: (    2*b+  c    )/3
11: (      b+2*c    )/3
12: (2*a        +  d)/3
13: (   2*b     +  d)/3
14: (       +2*c+  d)/3
15: (  a+  b    +  d)/3
16: (      b+  c+  d)/3
17: (  a+      c+  d)/3
18: (  a        +2*d)/3
19: (     b     +2*d)/3
20: (       +  c+2*d)/3
```

### Related Data and Programs:

NAVIER_STOKES_MESH3D, MATLAB data files defining tetrahedral meshes for several 3D test problems involving the Navier Stokes equations for flow flow, provided by Leo Rebholz.

TET_MESH_ORDER4, a dataset directory which contains examples of order 4 tetrahedral meshes.

TET_MESH_ORDER10, a dataset directory which contains examples of order 10 tetrahedral meshes.

TET_MESH_TO_GMSH, a MATLAB program which reads information defining a tet mesh, namely a file of node coordinates and a file of elements defined by node indices, and creates a corresponding Gmsh mesh file.

### Reference:

1. Herbert Edelsbrunner,
Geometry and Topology for Mesh Generation,
Cambridge, 2001,
ISBN: 0-521-79309-2,
LC: QA377.E36.

### Sample Files:

CYLINDER_3D is a mesh for 3D flow in a 0.41x2.5x0.41 channel, past a (square) cylinder, using 49,602 nodes and 9,792 elements.

STEP_3D is a mesh associated with 3D flow in a 10x50x10 channel, past a forward and backward step, using 38,992 nodes and 7,680 elements.

You can go up one level to the DATA page.

Last revised on 03 June 2013.