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Extensive experimental evidence highlights 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 superdiffusive nature of scalar turbulence. Subsequently, we develop a robust data-driven algorithm for estimation of the fractional (noninteger) Laplacian exponent, where we, on the fly, calculate the corresponding model coefficient employing a new dynamic procedure. Our a priori tests show that our new dynamically nonlocal LES paradigm provides better agreement with the ground-truth filtered direct numerical simulation data in comparison to the conventional static and dynamic Prandtl–Smagorinsky models. Moreover, in order to analyze the numerical stability and assessing the model's performance, we carry out comprehensive a posteriori tests. They unanimously illustrate that our new model considerably outperforms other existing functional models, correctly predicting the backscattering phenomena and, at the same time, 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 very large eddy simulation frameworks even with strong anisotropies, applicable to environmental applications.
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Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling
Nonlocal neural networks [25] have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of diffusion and damping effect of nonlocal networks by doing spectrum analysis on the weight matrices of the well-trained networks, and then propose a new formulation of the nonlocal block. The new block not only learns the nonlocal interactions but also has stable dynamics, thus allowing deeper nonlocal structures. Moreover, we interpret our formulation from the general nonlocal modeling perspective, where we make connections between the proposed nonlocal network and other nonlocal models, such as nonlocal diffusion process and Markov jump process.
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- PAR ID:
- 10100538
- Date Published:
- Journal Name:
- Advances in Neural Information Processing Systems 31 (NIPS 2018)
- Volume:
- 31
- Page Range / eLocation ID:
- 1-11
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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