Which tool/metric do you recommend to evaluate the quality and validity of a Large Eddy Simulation?

Question

The idea behind Large Eddy Simulation is to solve explicitely the scales of the flow that are resolved by the computational grid and to model the sub-grid scales. Ideally, the cut-off between these scales is located in the inertial range of the local turbulent field. This is because Kolmogorov's hypotheses predict a universal behavior of the turbulence in that inertial range and thus accurate modeling should be possible for the sub-grid scales. In practice, unless we consider a simple periodic box with isotropic turbulence, the cut-off between the resolved scales and the sub-grid does not occur in the inertial range for every point in the domain. Which begs the question: how can we know our current simulation is consistent with the LES framework?

Which method do you use to evaluate your LES? Does it matter whether you are using an implicit or explicit filtering of the small scales?

Answer 1

I'm not really an expert when it comes to LES, but I believe the following paper might be a good starting point:

"Assessment Measures for Engineering LES Applications" I. Celik, M. Klein, and J. Janicka, J. Fluids Eng. 131, 031102 (2009), DOI:10.1115/1.3059703

Answer 2

In a recent paper, Georgiadis et al. suggested a useful albeit limited approach. He first made the astute remark that usually, LES researchers run the finest mesh they can afford when dealing with somewhat complex geometries. Which leaves little leeway for exhaustive grid influence study. Note that I'm not using grid independence here since for an implicit LES this is mathematically absurd: changing the grid also affect your turbulence modeling, not just the numerics. Anyway, he suggested the following test:

If a solution has been obtained on a baseline computational mesh, then a coarser grid constructed by removing every other mesh point in each coordinate direction, will result in a solution requiring only one-eighth of the resources (assuming the time step is held constant) as that of the baseline. We believe this is a result worth obtaining.

He argues that if the results are qualitatively comparable, this is a good indication that the baseline LES is at least valid. On the other hand, if the coarse mesh simply crashes or yields obvious unphysical results, this might mean the original LES is not valid and requires more resolution.