Numerical and modeling error assessment of large-eddy simulation using direct-numerical-simulation-aided large-eddy simulation

TL;DR

This paper evaluates the numerical errors in large-eddy simulation (LES) of turbulence using a DNS-aided approach, revealing that numerical errors are comparable to modeling errors and highlighting their impact on SGS model development and wall modeling.

Contribution

It introduces a DNS-aided LES formulation that accurately assesses numerical errors, showing their significance relative to modeling errors in turbulence simulations.

Findings

Numerical errors are of the same order as modeling errors in LES.

Numerical errors near walls dominate in turbulent channel flow.

Supervised machine learning for SGS models may be less effective due to unaccounted numerical errors.

Abstract

We study the numerical errors of large-eddy simulation (LES) in isotropic and wall-bounded turbulence. A direct-numerical-simulation (DNS)-aided LES formulation, where the subgrid-scale (SGS) term of the LES is computed by using filtered DNS data is introduced. We first verify that this formulation has zero error in the absence of commutation error between the filter and the differentiation operator of the numerical algorithm. This method allows the evaluation of the time evolution of numerical errors for various numerical schemes at grid resolutions relevant to LES. The analysis shows that the numerical errors are of the same order of magnitude as the modeling errors and often cancel each other. This supports the idea that supervised machine learning algorithms trained on filtered DNS data might not be suitable for robust SGS model development, as this approach disregards the existence of numerical errors in the system that accumulates over time. The assessment of errors in turbulent channel flow also identifies that numerical errors close to the wall dominate, which has implications for the development of wall models.