Mesh: tet vs Hex -- CFD Online Discussion Forums

14 Oct.,2023

 

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There is plenty of information/discussion about this on the Internet. It's true you must be cautious with everything you read and confirm it yourself, however answers can give good starting points.

Tetrahedral elements can fit better complex geometry. However, when you integrate the shape functions with points of Gauss it is less accurate than hexahedral elements. In addition, one of the factors that determines the quality of your mesh is the distortion of your elements. The reason for this lays on the mapping from real to natural space of integration. To sum up, if your geometry is simple, the best option is to mesh it with hexahedral elements. If it is not possible (curved geometries, acute angles or similar) then go with tetrahedral but controlling the distortion of the elements.

Hexahedra meshes are also more economic with the number of elements because the same degrees of freedom (or for 8 nodes) for one hexahedron corresponds to six tetrahedra. It is obvious that increasing the number of elements will not increase the size of the global finite element matrices but the computations for one hexahedron are generated also for six tetrahedra. This step has to be compared in cpu time in order to state if it is interesting to use hexahedra than constant strain tetrahedra knowing that curved or linear hexahedra use Gauss integration points to generate the element characteristics (stiffness, mass, etc..) and tetrahedra use exact formula without any integration to get the same characteristics. Researchers have always used tetrahedra elements because they fit very well arbitrary shaped geometries with their simple computations.

In sum, it's a misconception that hexahedral elements are always better than tetrahedral.
Most old textbooks will tell you hexa (quad) mesh is better than tetra (tri) and show you how large the numerical errors may be introduced by tetra (tri) mesh. Sometimes, this is true, especially 15 or 20 years ago.

Historically, people prefer hex mesh due to: 1). At that time, only structured mesh can be used for most CFD solvers; 2). Less cell (element) count (so, a lot of saving in RAM and CPU time); 3). Unstructured solver was not matured.

The solver technology developments in most commercial FEA and CFD codes in the last decade have led to the similar results for hex and tetra mesh for most problems. Of course, tetra mesh usually needs more computing resources during solving stage. But his can be easily offset by the time saved in mesh generation. The accuracy advantage of hex mesh no longer exists anymore, for most engineering problems.

For some particular applications, e.g., wind turbine, pump, or aeroplane, hex mesh is still preferred, because of 1). Industry convention; 2). Well-understood physics (most users know how to align the mesh); 3). Special tools to generated hex mesh for such geometries.

However, for most FEA and CFD users, if the geometry is slightly complicated, it is just a waste to spend time on hex meshing. Your results will not be better, most of the time, if not always. The (solver) computing time saved with hex mesh is marginal compared with time wasted in mesh generation.

And yes, Ansys TurboGrid can automatically produce hexahedral meshes for all bladed components, i.e. the impeller

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