Tempered Fractional LES Modeling

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 Lévy-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 $\alpha \in (0,1)$, $\alpha \ne \frac{1}{2}$, 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.

arXiv comment28 pages, 10 figures, 3 tables

References in corpus (20)

• Exact Second-Order Structure-Function Relationships
• A Perspective on Machine Learning Methods in Turbulence Modelling
• Boundary problems for the fractional and tempered fractional operators
• Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime
• Non-locality and Intermittency in 3D Turbulence
• Dynamic Subgrid Scale Modeling of Turbulent Flows using Lattice-Boltzmann Method
• Data-driven learning of robust nonlocal physics from high-fidelity synthetic data
• Estimates of transition densities and their derivatives for jump Lévy processes
• High performance Python for direct numerical simulations of turbulent flows
• Self-attenuation of extreme events in Navier-Stokes turbulence
• Turbulence closure modeling with data-driven techniques: physical compatibility and consistency considerations
• A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence
• A Riesz basis Galerkin method for the tempered fractional Laplacian
• Interpreting neural network models of residual scalar flux
• A Unified Spectral Method for FPDEs with Two-sided Derivatives; A Fast Solver
• Turbulence Modeling via the Fractional Laplacian
• Anomalous Features in Internal Cylinder Flow Instabilities subject to Uncertain Rotational Effects
• Two-point stress-strain rate correlation structure and non-local eddy viscosity in turbulent flows
• Density estimates for sdes driven by tempered stable processes
• A Parallel Integrated Computational-Statistical Platform for Turbulent Transport Phenomena

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