The aspect ratio of the volume elements in Finite Volume Method
 

Hello people,

I have a question about the Finite Volume Method. Is the aspect ratio of the volume elements in Finite Volume Method important? The element aspect ratios are important in Finite Element Method, but I don't know if it's the case in FVM.

Thank you very much!

Yes you should try to keep the aspect ratio reasonable.

There are some exceptions, for example if you have a 2D grid and you extrude it in the third dimension to make it 3D the aspect ratio can typically be large as long as things aren't changing a lot in that direction.

For general problems, try to avoid very large aspect ratios whenever possible.

I have seen some authors who claimed that the ratio between two consecutive cells shouldn't be greater than 1.5. But it depends where and what for.
It seems that you limit the diffusion of the solution when the ratio is close to 1. However to manage with safety outflow boundaries,it is advised to extend the domain with expanded cells when you come closer to that boundaries.
For accuracy it seems better to keep as much as possible the ratio close to 1.

Hi,

it depends on the flow situation, cell type, solver, and the weather ...

For boundary layers (and most solvers), highly anisotropic cells do not pose a problem. On the contrary, you would not be able to fulfil the y+ <= 1 (or even 30-100) requirement without anisotropic cells.

I have also seen crisp shock waves which have been resolved by anisotropic tetras -- something that most people would tell you to avoid. If, however, you try to resolve a free shear layer with anisotropic tetras, you are quite likely to get an "NaN" as a reply ...

As a rule of thumb for most applications I would suggest to use anisotropic cells in the boundary layer only. Try to get the cells aligned as good as possible (i.e. use prisms or hexes).

Regards,
Oliver