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Tempered fractional LES modeling

Published online by Cambridge University Press:  02 December 2021

Mehdi Samiee ,
Ali Akhavan-Safaei Open the ORCID record for Ali Akhavan-Safaei [Opens in a new window]  and
Mohsen Zayernouri Open the ORCID record for Mohsen Zayernouri [Opens in a new window]
Mehdi Samiee
Affiliation:
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI 48824, USA
Ali Akhavan-Safaei
Affiliation:
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI 48824, USA
Mohsen Zayernouri*
Affiliation:
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA
*
†Email address for correspondence: zayern@msu.edu
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Abstract

The presence of non-local 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 modelling framework for developing non-local 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, $(\varDelta +\lambda )^{\alpha } (\cdot )$, 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, Phys. Fluids, vol. 6, issue 2, 1994, pp. 815–833). Finally, the model undergoes the a posteriori analysis to ensure the numerical stability and pragmatic efficiency of the model.

JFM classification

Turbulent Flows: Turbulence modelling Mathematical Foundations: Computational methods Nonlinear Dynamical Systems: Fractals
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 932 , 10 February 2022 , A4
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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