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
      

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

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.

• cylinder_3d_nodes.txt, the node file;
• cylinder_3d_elements.txt, the tetra file;

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.

• step_3d_nodes.txt, the node file;
• step_3d_elements.txt, the tetra file;

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