Multifractal subgrid-scale modeling for large-eddy simulation. II. Backscatter limiting and a posteriori evaluation

Results are presented from a posteriori evaluations of momentum and energy transfer between the resolved and subgrid scales when the multifractal subgrid-scale model from Part I is implemented in a flow solver for large-eddy simulations of turbulent flows. The multifractal subgrid-stress model is used to evaluate the subgrid part τ_ij* of the stress tensor, with the resolved part ū_iū_j evaluated by an explicit filter. It is shown that the corresponding subgrid and resolved contributions P* and P^R to the resolved-scale energetics produce extremely accurate results for the combined subgrid energy production field P(x,t). A separate backscatter limiter is developed here that removes spurious energy introduced in the resolved scales by including physical backscatter, without sacrificing the high fidelity in the stress and energy production fields produced by the multifractal subgrid-scale model. This limiter makes small reductions only to those components of the stress that contribute to backscatter, and principally in locations where the gradients are large and thus the energy introduced by numerical errors is also largest. Control of the energy introduced by numerical error is thus accomplished in a manner that leaves the modeling of the subgrid-scale turbulence largely unchanged. The multifractal subgrid-scale model and the backscatter limiter are then implemented in a flow solver and shown to provide stable and accurate results in a posteriori tests based on large-eddy simulations of forced homogeneous isotropic turbulence at cell Reynolds numbers ranging from 160 ≤ Re_Δ ≤10⁶, as well as in simulations of decaying turbulence where the model and the limiter must adjust to the changing subgrid conditions.