Computational Fluid Dynamics Using the Adaptive Wavelet-Collocation Method

Mehta, Yash; Nejadmalayeri, Ari; Regele, Jonathan D.

doi:10.3390/fluids6110377

Cited by 2 publications

(6 citation statements)

References 57 publications

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“…In contrast, the AWCM follows the Richardson hypothesis [77] and assumes that the fidelity of subgrid models depends on the local grid refinement to ensure that subgrid scales are approximately isotropic. Thus, both the AWCM and the CVS can drastically reduce the computational complexity of the turbulent flow simulation [17,35,107]. A large number of articles have demonstrated wavelet-based RANS, DES, and LES techniques for the numerical simulation of compressible and incompressible flows (e.g., the Ref.…”

Section: Conclusion and Future Directionmentioning

confidence: 99%

“…A large number of articles have demonstrated wavelet-based RANS, DES, and LES techniques for the numerical simulation of compressible and incompressible flows (e.g., the Ref. in [17]).…”

Section: Conclusion and Future Directionmentioning

confidence: 99%

“…Recently, the applications of wavelet transforms and machine learning in turbulence modeling have emerged as a promising area of investigation [10,17]. This review highlights two primary challenges in developing machine learning techniques for subgrid models of turbulence.…”

Section: Conclusion and Future Directionmentioning

confidence: 99%

“…In 2010, Schneider and Vasilyev [7] reviewed the application of wavelet transforms in computational fluid dynamics (CFD). Recently, Mehta et al [17] documented the new developments of the adaptive wavelet collocation method (AWCM) as a technique for solving partial differential equations (PDEs). Brunton et al [10] documented the concept of machine learning in fluid dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, simulations of homogeneous isotropic turbulence show that the Reynolds number scaling of CVS, O(Re 3 ), is slightly higher than that of AWCM (specifically WA-LES), O(Re 2.75 ). Recently, Mehta et al [17], Ge et al [8], and De Stefano and Vasilyev [35] covered a detailed review of turbulence modeling by the AWCM approach. Such studies primarily focused on the promise of wavelet compression and grid adaptation.…”

Section: Introductionmentioning

confidence: 99%

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Wavelet Transforms and Machine Learning Methods for the Study of Turbulence

Alam

2023

Fluids

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This article investigates the applications of wavelet transforms and machine learning methods in studying turbulent flows. The wavelet-based hierarchical eddy-capturing framework is built upon first principle physical models. Specifically, the coherent vortex simulation method is based on the Taylor hypothesis, which suggests that the energy cascade occurs through vortex stretching. In contrast, the adaptive wavelet collocation method relies on the Richardson hypothesis, where the self-amplification of the strain field and a hierarchical breakdown of large eddies drive the energy cascade. Wavelet transforms are computational learning architectures that propagate the input data across a sequence of linear operators to learn the underlying nonlinearity and coherent structure. Machine learning offers a wealth of data-driven algorithms that can heavily use statistical concepts to extract valuable insights into turbulent flows. Supervised machine learning needs “perfect” turbulent flow data to train data-driven turbulence models. The current advancement of artificial intelligence in turbulence modeling primarily focuses on accelerating turbulent flow simulations by learning the underlying coherence over a low-dimensional manifold. Physics-informed neural networks offer a fertile ground for augmenting first principle physics to automate specific learning tasks, e.g., via wavelet transforms. Besides machine learning, there is room for developing a common computational framework to provide a rich cross-fertilization between learning the data coherence and the first principles of multiscale physics.

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Section: Conclusion and Future Directionmentioning

confidence: 99%

“…A large number of articles have demonstrated wavelet-based RANS, DES, and LES techniques for the numerical simulation of compressible and incompressible flows (e.g., the Ref. in [17]).…”

Section: Conclusion and Future Directionmentioning

confidence: 99%

Section: Conclusion and Future Directionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Wavelet Transforms and Machine Learning Methods for the Study of Turbulence

Alam

2023

Fluids

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Wavelet Transforms and Machine Learning Methods for the Study of Turbulence

Alam¹

2023

Preprint

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This article examines the wavelet transforms and the machine learning methods in accelerating large eddy simulations of turbulent flows. An overarching challenge of large eddy simulations is to accurately represent the cascade of kinetic energy across the cut-off length scale. Taylor hypothesis suggests that the energy cascade occurs through the process of vortex stretching. However, Richardson hypothesis assumes the self-amplification of the strain field and a hierarchical break down of large eddies lead the energy cascade. The large eddy simulations typically employs the self-amplification of the strain in formulating subgrid models. However, several studies also proposed subgrid models based on vortex stretching. The wavelet-based coherent vortex simulation of turbulence directly accounts for vortex stretching in overall forward scatter of energy, while allowing local backscatter. The wavelet-based large eddy simulation adapts the grid to capture the creation of small-scale eddies, while adopting subgrid models based on the self-amplification of strain. The advancement of artificial intelligence in turbulence modelling is currently evolving around accelerating the numerical simulations of turbulent flow. However, there is a clear connection between the application of wavelet transfroms and neural networks for directly solving the Navier-Stokes equation, indicating some potential benefits of wavelet methods over the neural networks.

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Computational Fluid Dynamics Using the Adaptive Wavelet-Collocation Method

Cited by 2 publications

References 57 publications

Wavelet Transforms and Machine Learning Methods for the Study of Turbulence

Wavelet Transforms and Machine Learning Methods for the Study of Turbulence

Wavelet Transforms and Machine Learning Methods for the Study of Turbulence

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