A nested-LES wall-modelling approach for high Reynolds number wall-bounded turbulence

A new wall-modelling approach for LES of high Reynolds number wall-bounded turbulence is proposed. The method couples coarse-grained LES in a full-size channel with nested fine-grained LES in a minimal channel. At each iteration, the fluctuating velocity field in both channels is rescaled to match the TKE components to that of the minimal channel in the near-wall region ($z^+<100$), to that of the full-size channel in the core ($z^+>300$), and to a weighted average of the two in between. Results were insensitive to the details and width of the weighting function. Simulations were performed for $1000\le Re_\tau \le 10,000$ in full channels of size $2 \pi h \times \pi h \times 2h$ and minimal channels of size $3000 \times 1500 \times 2Re_\tau$ wall units in the streamwise, spanwise and wall-normal directions, respectively. At all $Re_\tau$, resolutions of $64\times64\times65$ in the full-size channel and $32\times64\times65$ in the minimal channel were employed, rendering the cost of computations independent of $Re_\tau$. The Dynamic Smagorinsky model was used as the SGS model. The results show that the nested-LES approach can predict a friction coefficient within $5\%$ of Dean's correlation, and one-point statistics in good agreement with available DNS and experimental data.