An alternative derivation of the Germano identity as the residual of the LES equation

TL;DR

This paper offers a new derivation of the Germano identity, interpreting its error as the residual of the LES equation, which aids in error estimation and grid adaptation in large eddy simulations.

Contribution

It provides an alternative derivation and interpretation of the Germano identity, linking its error directly to the LES residual and enhancing error analysis methods.

Findings

Germano identity error estimates LES residuals

Supports improved grid and filter adaptation

Facilitates uncertainty quantification in LES

Abstract

The Note presents an alternative derivation and interpretation of the Germano identity and its error, showing that the Germano identity error directly estimates the residual of the LES equation, i.e., the misfit when evaluating the inexact equation for the exact solution, and therefore represents the source of errors in LES. This has many applications, including for optimal output-based grid/filter-adaptation and uncertainty quantification in LES.