A dynamic localization model for large-eddy simulation of turbulent flows

TLDR

The Germano et al. (1991) method computes subgrid‑scale eddy viscosity coefficients as functions of space and time, offering a self‑calibrating approach that requires no a priori coefficients or wall‑damping functions. This study addresses the mathematical inconsistencies and limitations of that method by proposing a rectified formulation. The new formulation derives an integral equation whose solution yields the coefficient at each position and time, and it has been validated in isotropic turbulence and a backward‑facing step.

Abstract

In a previous paper, Germano, et al. (1991) proposed a method for computing coefficients of subgrid-scale eddy viscosity models as a function of space and time. This procedure has the distinct advantage of being self-calibrating and requires no a priori specification of model coefficients or the use of wall damping functions. However, the original formulation contained some mathematical inconsistencies that limited the utility of the model. In particular, the applicability of the model was restricted to flows that are statistically homogeneous in at least one direction. These inconsistencies and limitations are discussed and a new formulation that rectifies them is proposed. The new formulation leads to an integral equation whose solution yields the model coefficient as a function of position and time. The method can be applied to general inhomogeneous flows and does not suffer from the mathematical inconsistencies inherent in the previous formulation. The model has been tested in isotropic turbulence and in the flow over a backward-facing step.