Tempered Fractional LES Modeling

TL;DR

This paper introduces a novel tempered fractional LES model based on nonlocal turbulence effects, employing tempered Lévy distributions and fractional Laplacians, validated through statistical and numerical analyses for improved turbulence simulation.

Contribution

It develops a tempered fractional-order framework for LES, deriving a new nonlocal subgrid-scale model with proven invariance and efficiency, advancing turbulence modeling techniques.

Findings

The model accurately captures nonlocal turbulence effects.

It demonstrates numerical stability and improved efficiency.

The approach aligns with theoretical invariance properties.

Abstract

The presence of nonlocal interactions and intermittent signals in the homogeneous isotropic turbulence grant multi-point statistical functions a key role in formulating a new generation of large-eddy simulation (LES) models of higher fidelity. We establish a tempered fractional-order modeling framework for developing nonlocal LES subgrid-scale models, starting from the kinetic transport. We employ a tempered L\'evy-stable distribution to represent the source of turbulent effects at the kinetic level, and we rigorously show that the corresponding turbulence closure term emerges as the tempered fractional Laplacian, $(\Delta+\lambda)^{\alpha} (\cdot)$, for $\alpha \in (0,1)$, $\alpha \neq \frac{1}{2}$, and $\lambda>0$ in the filtered Navier-Stokes equations. Moreover, we prove the frame invariant properties of the proposed model, complying with the subgrid-scale stresses. To characterize the optimum values of model parameters and infer the enhanced efficiency of the tempered fractional subgrid-scale model, we develop a robust algorithm, involving two-point structure functions and conventional correlation coefficients. In an a priori statistical study, we evaluate the capabilities of the developed model in fulfilling the closed essential requirements, obtained for a weaker sense of the ideal LES model (Meneveau 1994). Finally, the model undergoes the a posteriori analysis to ensure the numerical stability and pragmatic efficiency of the model.