Meshing of volumes algorithms


Flux provides three generators for automatic meshing of volumes: the Delaunay mesher, the Netgen mesher and the MeshGems mesher.

The three meshers are presented in the blocks below.

Delaunay mesher: process

The mesh generation by the Delaunay mesher is carried out in two phases, as presented in the table and figure below.

Stage Description
1 Generation of boundary mesh
2 Insertion of internal nodes into border mesh elements

MeshGems mesher: process

MeshGems, by its module MG-Tetra it is a generator of tetrahedral mesh of volume from a mesh of surface triangular. It is marketed by Distene

Comparison between Delaunay and MeshGems is presented in the table below.

  Delaunay MeshGems
  • This mesher is the historical mesher of Flux
  • Potentially it rebuild the surface mesh to construct a mesh of volume
  • Respects the surface mesh (not node insertion)
  • Robust mesher=> tested by other simulation tools

Advantages /


  • Relaxation may be important =>Less nodes and less mesh elements
  • More time to mesh the device
  • Difficulty with the extrusive mesh
  • Low relaxation => Increase the number of nodes and the number of mesh elements
  • Low time to mesh the device with good quality of the mesh compared to Delaunay
  • Suitable for mixed mesh

* Reminder: In 3D, in case of a mixed meshing (mapped mesh /automatic mesh) with the Delaunay mesher, certain nodes must be inserted on the faces during the generation of the mesh front. This insertion is forbidden on the mapped faces, which generates the failure of the Delaunay mesher. The Netgen mesher is better suited to this problem.

Netgen mesher: process

The mesh generation by the Netgen mesher is an iterative process that is carried out in several phases, as presented in the table and figure below.

Stage Description
1 Initialization of front on the domain boundary
2 The front becomes the border between the meshed region and the non-meshed region

At each iteration:

  • covering of the domain by the front (creation of one layer of elements)
  • actualization of the domain front
4 Stop the process when the domain is entirely meshed

Note: This mesher will not be available in future versions

Mesh optimization

Independent of the choice of mesher, Flux equally provides an algorithm for the optimization of the automatic volume meshing.

The optimization enables:

  • to improve the mesh quality
  • to reduce the number of elements

Optimization of the process

The mesh optimization is an iterative process of partition and/or fusion of the volume elements in function by certain predefined criteria. The global goal is the improvement of the mesh quality and the reduction of the number of elements.

The number of iterations influences over the quality of the result and the process time:

  • Optimization of average quality and rapid: one iteration
  • Optimization of good quality and slow: five iterations

The default number of iterations is set to 3, a value permitting to obtain a good quality/time ratio.