Consistent closure modeling in large eddy simulations by direct approximation of the filtered advection term

TL;DR

This paper identifies a conceptual inconsistency in LES related to the advection term and proposes a direct approximation method based on an infinite series expansion, leading to improved simulation results.

Contribution

It introduces a novel, consistent approach to approximate the filtered advection term in LES using an infinite series expansion, enhancing accuracy and mesh independence.

Findings

Improved kinetic energy spectra in LES simulations.

Enhanced filtered velocity correlations.

Better agreement with theoretical expectations.

Abstract

This article addresses the widely overlooked conceptual inconsistency of the large eddy simulation (LES) framework, namely that the commonly used advection term introduces higher wave numbers in the filtered Navier-Stokes equations than consistent with the definition of a filtered equation. It is explained how this inconsistency is the reason that flux limiters, stabilization terms, or dealiasing is often required and that the LES solution is typically mesh dependent. A consistent alternative is the direct approximation of the filtered advection term, for which we derive an exact expression based on an infinite series expansion with terms of increasing order in the filter width. We show that truncating the series expansion after few terms gives an expression that is highly correlated with the filtered advection term and a suitable LES model. A posteriori studies with decaying turbulence and a turbulent shear flow are conducted that reveal that the proposed approximation of the filtered advection term predicts improved kinetic energy spectra and filtered velocity correlations compared to classical LES.