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In this study, we revisit the spectral transfer model for the turbulent intensity in passive scalar transport (under large-scale anisotropic forcing), and a subsequent modification to the scaling of scalar variance cascade is presented. From the modified spectral transfer model, we obtain a revised scalar transport model using a fractional-order Laplacian operator that facilitates the robust inclusion of the non-local effects originating from large-scale anisotropy transferred across the multitude of scales in the turbulent cascade. We provide ana prioriestimate for the non-local model based on the scaling analysis of the scalar spectrum, and later examine our developed model through direct numerical simulation. We present a detailed analysis on the evolution of the scalar variance, high-order statistics of the scalar gradient and important two-point statistical metrics of the turbulent transport to make a comprehensive comparison between the non-local model and its standard version. Finally, we present an analysis that seamlessly reconciles the similarities between the developed model with the fractional-order subgrid-scale scalar flux model for large-eddy simulation (Akhavan-Safaeiet al.,J. Comput. Phys., vol. 446, 2021, 110571) when the filter scale approaches the dissipative scales of turbulent transport. In order to perform this task, we employ a Gaussian process regression model to predict the model coefficient for the fractional-order subgrid model.
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A Parallel Computational–Statistical Framework for Simulation of Turbulence: Applications to Data-Driven Fractional Modeling
In this work, an open-source computational–statistical platform to obtain synthetic homogeneous isotropic turbulent flow and passive scalar transport is presented. A parallel implementation of the well-known pseudo-spectral method in addition to the comprehensive record of the statistical and small-scale quantities of the turbulent transport are offered for executing on distributed memory CPU-based supercomputers. The user-friendly workflow and easy-to-run design of the developed package are disclosed through an extensive and step-by-step example. The resulting low- and high-order statistical records vividly verify a well-established and fully developed turbulent state as well as the seamless statistical balance of conservation laws. The post-processing tools provided in this platform would allow the user to easily construct multiple important transport quantities from primitive turbulent fields. The programming codes for this tool are accessible through GitHub (see Data Availability Statement).
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- Award ID(s):
- 1923201
- PAR ID:
- 10494622
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Fractal and Fractional
- Volume:
- 7
- Issue:
- 6
- ISSN:
- 2504-3110
- Page Range / eLocation ID:
- 488
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/fractalfract7060488
