调和分数阶大涡模拟建模
Tempered Fractional LES Modeling
AI总结：
本文提出调和分数阶大涡模拟建模框架，从动理学输运出发推导出调和分数阶拉普拉斯闭合项，并验证其框架不变性、参数优化及先验与后验性能，以提升LES模型保真度。
摘要：
在均匀各向同性湍流中，非局部相互作用和间歇信号的存在使得多点统计函数在构建新一代更高保真度的大涡模拟（LES）模型中扮演关键角色。我们从动理学输运出发，建立了一个调和分数阶建模框架，用于开发非局部LES亚格子模型。我们采用调和Lévy稳定分布来表征动理学层面湍流效应的来源，并严格证明相应的湍流闭合项在滤波后的Navier-Stokes方程中表现为调和分数阶拉普拉斯算子$(Δ+λ)^α (\cdot)$，其中$α∈(0,1)$，$α≠\frac{1}{2}$，且$λ>0$。此外，我们证明了所提出模型的框架不变性，符合亚格子应力的要求。为了表征模型参数的最优值并推断调和分数阶亚格子模型的增强效率，我们开发了一种稳健的算法，涉及两点结构函数和常规相关系数。在一项先验统计研究中，我们评估了所开发模型在满足闭合基本要求方面的能力，这些要求是在较弱意义上针对理想LES模型（Meneveau 1994）获得的。最后，该模型经过后验分析，以确保模型的数值稳定性和实际效率。
英文摘要：
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, $(Δ+λ)^α (\cdot)$, for $α\in (0,1)$, $α\neq \frac{1}{2}$, and $λ>0$ 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.
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