Some questions about implicit LES

Hi, everyone

I wonder can a DNS code directly be used to perform ILES without any revision. The difference between DNS and ILES is the requirement of mesh resolution from the view of implemention, right? Moreover, does the ILES have the procedure of filtering? What properties are needed for the numerical scheme to be suitable for ILES?

Best regards

Not all DNS schemes are suitable for ILES; it depends on their dispersion and dissipation relationship. Namely, that unresolved scales need to be subject to a reasonable degree of dissipation. The FR schemes used by PyFR are suitable without any modification.

Regards, Freddie.

Further to this, there is no filtering in ILES as the filter is implicit from the numerical scheme. If you were to set a filter explicitly then you are on the road to LES. Consider “Turbulent Flows” by Pope, chapter 13.

What properties are needed from a numerical scheme to be suitable for ILES is a more tricky question. Ultimately, you need a numerical scheme that has increased numerical dissipation at high frequencies. Also high order is useful as it allows for a decoupling of truncation and aliasing error in terms of grid spacing. But the thing to remember with ILES is once you have a numerical method set, the filter is then controlled by the grid, hence why mesh can be very important.

Sometimes a better way of thinking about ILES is as under-resolved DNS. When you think of it like this you can see that many methods suitable for DNS may not be suitable for ILES. Primarily as they have no implicit way of damping/controlling/modelling those unresolved features.

Some good reference worth considering are: Chow and Moin and Ghosal.

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Thank you for your kind reply! As you mentioned, the filter is controlled by the grid and mesh can be very important. Is it meaningful to do grid independence study since the grid has a significant impact on the results in ILES?

Yes. The hypothesis behind LES is that one only needs to resolve the large scale structures to obtain measurements which are suitable for typical engineering purposes. However, what counts as a ‘large’ structure is not clear cut and the importance of resolving a specific structure depends very much on the geometry of the problem and what quantities are being measured. As such a grid convergence study is still required.

Regards, Freddie.

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