Basic meshing algorithms

The MESH module contains a set of meshing algorithms, which are used for meshing entities (1D, 2D, 3D sub-shapes) composing geometrical objects.

An algorithm represents either an implementation of a certain meshing technique or an interface to the whole meshing program generating elements of several dimensions.

• For meshing of 1D entities (edges):

  • Wire Discretization meshing algorithm - splits an edge into a number of mesh segments following an 1D hypothesis.
  • Composite Side Discretization algorithm - allows to apply a 1D hypothesis to a whole side of a geometrical face even if it is composed of several edges provided that they form C1 curve in all faces of the main shape.

• For meshing of 2D entities (faces):

  • Triangle: Mefisto meshing algorithm - splits faces into triangular elements.
  • Quadrangle: Mapping meshing algorithm - splits faces into quadrangular elements.
  

  Example of a triangular 2D mesh
  

  Example of a quadrangular 2D mesh

• For meshing of 3D entities (solid objects):

  • Hexahedron (i,j,k) meshing algorithm - solids are split into hexahedral elements thus forming a structured 3D mesh. The algorithm requires that 2D mesh generated on a solid could be considered as a mesh of a box, i.e. there should be eight nodes shared by three quadrangles and the rest nodes should be shared by four quadrangles.

    

    Structured mesh generated by Hexahedron (i,j,k) on a solid bound by 16 faces

  • Body Fitting meshing algorithm - solids are split into hexahedral elements forming a Cartesian grid; polyhedra and other types of elements are generated where the geometrical boundary intersects Cartesian cells.
  

  Example of a tetrahedral 3D mesh
  

  Example of a hexahedral 3D mesh

Some 3D meshing algorithms, such as Hexahedron(i,j,k) also can generate 3D meshes from 2D meshes, working without geometrical objects.

There is also a number of more specific algorithms:

• Extrusion 3D - for meshing prismatic 3D shapes with hexahedra and prisms.
• Quadrangle: Medial Axis Projection - for quadrangle meshing of faces with sinuous borders and rings.
• Polygon per Face meshing algorithm - generates one mesh face (either a triangle, a quadrangle or a polygon) per a geometrical face using all nodes from the face boundary.
• Projection algorithms - for meshing by projection of another mesh.
• Import algorithms - for meshing by importing elements from another mesh.
• Radial Prism - for meshing 3D geometrical objects with cavities with hexahedra and prisms.
• Radial Quadrangle 1D-2D - for quadrangle meshing of disks and parts of disks.
• Use Faces/Edges to be Created Manually - to create a 1D or a 2D mesh in a python script.
• Segments around Vertex - for defining the length of mesh segments around certain vertices.

Constructing meshes page describes in detail how to apply meshing algorithms.

See Also a sample TUI Script of a Define Meshing Algorithm operation.