Dynamic Nonlocal Passive Scalar Subgrid-Scale Turbulence Modeling

TL;DR

This paper introduces a novel nonlocal LES model for scalar turbulence that uses a fractional Laplacian to better capture anomalous diffusion and intermittency, outperforming traditional models in accuracy and stability.

Contribution

The paper develops a dynamic, data-driven nonlocal LES framework based on fractional calculus for scalar turbulence, improving modeling of super-diffusive behavior and backscattering phenomena.

Findings

Better agreement with DNS data than traditional models.

Outperforms existing models in stability and accuracy.

Effectively predicts backscattering and small-to-large scale correlations.

Abstract

Extensive experimental evidence highlight that scalar turbulence exhibits anomalous diffusion and stronger intermittency levels at small scales compared to that in fluid turbulence. This renders the corresponding subgrid-scale dynamics modeling for scalar turbulence a greater challenge to date. We develop a new large eddy simulation (LES) paradigm for efficiently and dynamically nonlocal LES modeling of the scalar turbulence. To this end, we formulate the underlying nonlocal model starting from the filtered Boltzmann kinetic transport equation, where the divergence of subgrid-scale scalar fluxes emerges as a fractional-order Laplacian term in the filtered advection-diffusion model, coding the corresponding supper-diffusive nature of scalar turbulence. Subsequently, we develop a robust data-driven algorithm for estimation of the fractional (non-integer) Laplacian exponent, where we on-the-fly calculate the corresponding model coefficient employing a new dynamic procedure. Our $\textit{a priori}$ tests show that our new dynamically nonlocal LES paradigm provides better agreements with the ground-truth filtered DNS data in comparison to the conventional static and dynamic Prandtl-Smagorisnky models. Moreover, in order to analyze the numerical stability and assessing the model's performance, we carry out a comprehensive $\textit{a posteriori}$ tests. They unanimously illustrate that our new model considerably outperforms other existing functional models, correctly predicting the backscattering phenomena at the same time and providing higher correlations at small-to-large filter sizes. We conclude that our proposed nonlocal subgrid-scale model for scalar turbulence is amenable for coarse LES and VLES frameworks even with strong anisotropies, applicable to environmental applications.