A model for subgrid Reynolds stress anisotropy to enable coarse large eddy simulation

Reliable large eddy simulation (LES) is often intractable for complex

turbulent flows of technological interest due to the need to resolve

deep into the inertial range. However, this resolution requirement is

not fundamental to LES, but is instead a result of subgrid scale models

being formulated to represent only the transfer of energy to the

subgrid scales while ignoring all other statistical roles of the

subgrid turbulence. Such models require both the true subgrid

Reynolds stress and the stress arising from the subgrid

scale model to be dynamically negligible. It is this requirement that

is primarily responsible for the high resolution. To enable tractable

LES, the statistical role of subgrid scale models must be expanded

beyond dissipation. Further complicating the application of LES is

the anisotropy of the subgrid turbulence when the resolution is

coarse, which is inconsistent with classic scalar eddy-viscosity model

forms. Here, we propose a gradient- and strain-energy-density

similarity-based model form for the subgrid Reynolds stress anisotropy

which is entirely divorced from the energy transfer role. The model

uses data generated from multiple homogeneous anisotropic turbulence

in-a-box simulations to determine model coefficients as functions of

invariants of resolved statistics and is shown to perform well over

all potential filter widths.