I wrote about SGS models for LES about eight years ago. In that post, ILES was advocated for wall-resolved LES with dissipative high-order methods such as the discontinuous Galerkin, spectral difference, and flux reconstruction (FR) methods. Many groups, including us, showed that adding SGS models produced worse results than ILES compared to DNS results.
We did find an outlier earlier this year. An SGS model improved the results of LES of the turbulent channel flow with a 6th-order (P5) FR scheme. A further investigation leads to a deeper understanding of SGS models in LES. Here are the main findings:
- The SGS stress is a 2nd-order term with respect to the filter size or mesh size. This means any schemes higher than 2nd order do not have enough dissipation to damp the sub-grid scales, resulting in energy pileups near the cut-off wave number as shown in Figure 1.
Figure 1. Energy spectra for ILES of Burgers turbulence with different P orders
- The energy pileups for P2, P3 and P4 schemes appear to improve the prediction of the wall skin friction compared to the DNS results. In other words, the unphysical energy addition due to unresolved scales appears to compensate for the energy loss (relative to DNS) due to the LES filtering, resulting in a better agreement with DNS data. Any damping of these pileups pushes the results further away from the DNS data.
- On the other hand, the P5 scheme over-compensated for the energy loss, and the addition of an SGS model can achieve a better agreement with DNS data. This also means that very coarse meshes can be used with the P5 scheme to achieve DNS-like results with a properly calibrated SGS model.
In summary, use ILES with any schemes lower than 6th order (P2-P4), but use an SGS model with 6th or higher order schemes (P > 4). The findings will be presented in SciTech 2026 at Orlando. I will also play pickleball in Orlando Racket Sports. If you are interested in learning or playing pickleball in Orlando, do let me know.
