Evaluation of explicit and implicit LES closures for Burgers turbulence

TL;DR

This paper evaluates the accuracy of explicit and implicit LES closure models for Burgers turbulence, introducing new filters and algorithms to improve convergence and energy spectrum prediction.

Contribution

It introduces novel discrete binomial smoothing filters and an enhanced Van Cittert algorithm, advancing LES closure modeling for Burgers turbulence.

Findings

Implicit high-order schemes effectively converge to DNS at higher resolutions.

The models accurately capture energy content near grid cut-off scales.

New filtering techniques improve convergence of deconvolution processes.

Abstract

In this work, we perform an aposteriori error analysis on implicit and explicit large eddy simulation closure models for solving the Burgers turbulence problem. Our closure modeling efforts include both functional and structural models equipped with various low-pass filters. We introduce discrete binomial smoothing filters and an enhanced version of the Van Cittert algorithm to accelerate the convergence of approximate deconvolution processes including regularization and relaxation filtering approaches. Our implicit modeling efforts consist of various high-order schemes including compact and non-compact fifth-order upwind schemes as well as weighted essential non-oscillatory (WENO) and compact reconstructed WENO (CRWENO) schemes, and the resulting schemes are shown to effectively converge to the direct numerical simulation (DNS) for increasing resolutions. Comparing with DNS and underresolved DNS computations, our numerical assessments illustrate the ability of these methods to capture the energy content near grid cut-off scale.