Numerical error of explicitly filtered large-eddy simulation for consistent data-driven modeling

Data-driven techniques have been widely adopted in subgrid-scale (SGS) modeling of large-eddy simulations (LES) and show promising performance in a priori tests. However, the application of the data-driven models to simulations in the a posteriori tests is not necessarily consistent with a priori results. The inconsistency is partially due to extra numerical terms when using filtered direct numerical simulation (DNS) data for training the LES SGS stress term.

We separate the contribution of the SGS modeling and the numerical terms in LES, where the numerical term is a combination of commutation error, discretization of operators, and resolution truncation. DNS data from forced isotropic turbulence will be used for analysis. We study the effect of explicit filtering on both the SGS stress and the numerical term. We show that explicit filtering is crucial for reducing the contribution of the numerical term, and thus, obtaining a consistent data-driven model.