[DeadLee]

Hi all,

I'm coming from a Finite Element Analysis background and have been wondering about the influences of the different types of cell shapes and their influence on results in CFD.

For example, in most formulations of FEM:
-3D elements are missing the rotational degrees of freedom so interfaces with 2D plate elements have to be handed correctly
- hexas behave poorly in bending if we're not careful (shear locking)
- 2D elements don't have the 6th degree of freedom (out of plane rotation) so that has to taken into account for some geometries
-etc

The advantages and disadvantages of each type should be considered depending on the problem before meshing.

TLDR: I'm wondering what characteristics each element type has. Especially for transitions; do prism > hexa transitions behave as expected? Does the orientation of the prism elements w.r.t to the flow have an impact? And tetra> prisms? Is it the same in 2D and 3D?


In my case I'm using openFoam to simulate a vertical wxis wind tubrine (rotating mesh), so high Re with flow separation.

[sbaffini]

Originally Posted by DeadLee

Hi all,

I'm coming from a Finite Element Analysis background and have been wondering about the influences of the different types of cell shapes and their influence on results in CFD.

For example, in most formulations of FEM:
-3D elements are missing the rotational degrees of freedom so interfaces with 2D plate elements have to be handed correctly
- hexas behave poorly in bending if we're not careful (shear locking)
- 2D elements don't have the 6th degree of freedom (out of plane rotation) so that has to taken into account for some geometries
-etc

Thank God we have none of this b...t in finite volume (sorry, someone had to say this ).

Jokes apart, very generally speaking, in mixed order:

- We don't mix (typically) 2D and 3D cells in the finite element sense. If your grid is 3D all your cells are 3D. End of the story. You need to look at the Finite volume approach as writing a conservation law for each cell. There are some corner cases like, say, a 3d grid that at the inlet/outlet is coupled with a 1d grid, but everything works as expected when you properly take into account the conservation laws

- As above, a finite volume code can handle general polyhedral grids and will work as expected as long as proper conservation laws are taken into account at grid interfaces. If the interface is conformal it is just an ordinary job; if it isn't, then the faces on both sides need to be first split and rearranged to have an exact 1-to-1 or n-to-1 coupling. Not sure what you mean by prism cells, but in FV CFD they can exactly match an hexa only if they are hexa themselves

- What matters the most in a cell centered FV grid is the alignment between neighbor cell centers and the normal on their common face; you don't necessarily loose accuracy if this goes bad, but everything becomes more unstable because that misalignment is typically handled explicitly

- Error is proportional to the solution and its derivative when computing fluxes on the cell faces. If the flow is aligned with the grid (prism or not) you get 0 error on some faces. If the grid is hexa, uniform and aligned you may get that some error terms cancel from opposite faces (so aligned hexa are always better if achievable... tetra bad).

- 2D and 3D are basically the same in principle

[DeadLee]

Originally Posted by sbaffini

Thank God we have none of this b...t in finite volume (sorry, someone had to say this ).

Haha now I'm glad about that too!

Thanks for your detailed reply, all questions (and some more I didn't ask) answered!

(for the prism hexa, imagine a mixed 2D tria/quad mesh extruded in one direction, you get a mixed prism/hexa mesh)