# Minimum possible element size

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 February 12, 2016, 05:59 Minimum possible element size #1 Member   Join Date: Nov 2014 Posts: 36 Rep Power: 11 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?

February 12, 2016, 06:12
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Filippo Maria Denaro
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Quote:
 Originally Posted by Tscar 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

 February 12, 2016, 09:01 #3 Super Moderator     Alex Join Date: Jun 2012 Location: Germany Posts: 3,412 Rep Power: 49 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. Tscar likes this.

February 12, 2016, 13:50
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 Originally Posted by flotus1 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 ...

 Tags element size, finite volume method