Multifractal subgrid-scale modeling for large-eddy simulation. I. Model development and a priori testing

Abstract

Results are presented from a new approach to modeling the subgrid-scale stresses in large-eddy simulation of turbulent flows, based on explicit evaluation of the subgrid velocity components from a multifractal representation of the subgrid vorticity field. The approach is motivated by prior studies showing that the enstrophy field exhibits multifractal scale-similarity on inertial-range scales in high Reynolds number turbulence. A scale-invariant multiplicative cascade thus gives the spatial distribution of subgrid vorticity magnitudes within each resolved-scale cell, and an additive cascade gives the progressively isotropic decorrelation of subgrid vorticity orientations from the resolved scale ΔΔ to the viscous scale λνλν. The subgrid velocities are then obtained from Biot–Savart integrals over this subgrid vorticity field. The resulting subgrid velocity components become simple algebraic expressions in terms of resolved-scale quantities, which then allow explicit evaluation of the subgrid stresses τij*τij*. This new multifractal subgrid-scale model is shown in a priori tests to give good agreement for the filtered subgrid velocities, the subgrid stress components, and the subgrid energy production at both low (ReΔ ≈ 160)(ReΔ≈160) and high (ReΔ ≈ 2550)(ReΔ≈2550) resolved-scale Reynolds numbers. Implementing the model is no more computationally burdensome than traditional eddy-viscosity models. Moreover, evaluation of the subgrid stresses requires no explicit differentiation of the resolved velocity field and is therefore comparatively unaffected by discretization errors.