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

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.