A resolvable subfilter-scale model specific to large-eddy simulation of under-resolved turbulence

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Abstract
Large-eddy simulation (LES) of boundary-layer flows has serious deficiencies near the surface when a viscous sublayer either does not exist (rough walls) or is not practical to resolve (high Reynolds numbers). In previous work, we have shown that the near-surface errors arise from the poor performance of algebraic subfilter-scale (SFS) models at the first several grid levels, where integral scales are necessarily under-resolved and the turbulence is highly anisotropic. In under-resolved turbulence, eddy viscosity and similarity SFS models create a spurious feedback loop between predicted resolved-scale (RS) velocity and modeled SFS acceleration, and are unable to simultaneously capture SFS acceleration and RS–SFS energy flux. To break the spurious coupling in a dynamically meaningful manner, we introduce a new modeling strategy in which the grid-resolved subfilter velocity is estimated from a separate dynamical equation containing the essential inertial interactions between SFS and RS velocity. This resolved SFS (RSFS) velocity is then used as a surrogate for the complete SFS velocity in the SFS stress tensor. We test the RSFS model by comparing LES of highly under-resolved anisotropic buoyancy-generated homogeneous turbulence with a corresponding direct numerical simulation (DNS). The new model successfully suppresses the spurious feedback loop between RS velocity and SFS acceleration, and greatly improves model predictions of the anisotropic structure of SFS acceleration and resolved velocity fields. Unlike algebraic models, the RSFS model accurately captures SFS acceleration intensity and RS–SFS energy flux, even during the nonequilibrium transient, and properly partitions SFS acceleration between SFS stress divergence and SFS pressure force.