A multifractal subgrid-scale model for the large-eddy simulation of turbulent flows

The present work develops a fundamentally new theoretical and numerical approach to modeling the subgrid-scale stresses for the large-eddy simulation (LES) of turbulent flows, which incorporates significant subgrid physics, yet can be implemented readily in the spatial domain. The approach draws on the multifractal structure of the enstrophy field in the inertial-range scales of turbulence to describe the spatial distribution of vorticity within the subgrid field. It is then possible to recast the subgrid-velocity contributions $usgsi$ to the subgrid stresses τ_ij as Biot-Savart integrals over the subgrid-vorticity field, permitting direct calculation of τ_ij. The model can be simplified using central-limit concepts, and at high Reynolds-number, the subgrid-velocity field $usgsi$ reduces to a simple algebraic form based on quantities available from the resolved flow field in an LES calculation. Results from a priori tests are presented indicating good agreement between model and DNS values for τ_ij and subgrid-energy production $Psgs$ in both lower and higher Reynolds-number cases. The work also describes the backscatter limiter, a new method to manage resolved energy and stabilize LES calculations by limiting those stresses contributing to backscatter. The results of actual large-eddy simulations using the multifractal model are then presented, indicating that the multifractal model runs stably at very-high Reynolds-numbers and recovers important characteristics of real turbulence, including the k−5/3 scaling of the energy spectrum E(k), the distributions of the velocity-gradient and fluctuation-stress tensors, as well as the high intermittency seen in real turbulent flows. Finally, the work derives multifractal models for the subgrid-scalar concentrations $zsgs$ in the filtered passive-scalar transport equation and the Reynolds stresses in the Reynolds-Averaged Navier-Stokes (RANS) equations.