Minimum possible element size
 

Hi,

I have a question relating minimum element size that can be used in CFD.

I understand that there are problems in microscale where the hypothesis of continuum can not be used. For example, for gases, in a system which has length scale of the order of hundreds nanometers (i.e. comparable to the mean free path).

But if I have a macroscale system, where I can get appropriate solution by means of finite volume method, is there a limit of how small elements I can use in discretization? Can I have a minimum element width on the order of nanometers and still get the "right" solution, even though the balance equations I solve for those small elements do not in fact apply on them?

In principle, when you work in the non-dimensional form of the equation, the domain has computational lenghts of O(1), therefore no matter about the computational precision. As you stated, the limit is in the respect of the continuosu model, I suppose in standard condition no smaller than O(10^-8) meters

Given enough computational resources and leaving aside the problems with round-off errors, you can use cell/element sizes much smaller than the mean free path and still get the correct solution to the macroscopic set of equations you are solving.
A numerical algorithm for solving the Navier-Stokes equations is completely unaware of the physics that these equations fail to describe.

Thank you. I thought so to.

Is that true even if I use turbulent models? I think viscous heating might not be handled well in such cases ...