Effects of time-filtering the Navier–Stokes equations

Oberle, Daniel; Pruett, C. David; Jenny, Patrick

doi:10.1063/5.0152642

Cited by 4 publications

(3 citation statements)

References 21 publications

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“…where we search for a subgrid-scale stress τ ij as an approximation of the subfilter-scale stress τ s ij . We emphasize that subgrid-scale stresses are not the same as true subfilter-scale stresses [18,19]. Thus, the temporal evolution of the large-scale dynamics of a fluid system is given by…”

Section: The Filtered Navier-stokes Systemmentioning

confidence: 99%

“…We know that the commutativity (of filtering and differentiation) is natural for a temporal filter, which remains problematic for spatial ones. The temporally filtered Navier-Stokes equations remain frame-invariant under the Galilean group of transformations [19,98]. Thus, minimizing the Lagrangian Equation ( 15) must faithfully resolve a significant fraction of the subfilter-scale stress τ s ij .…”

Section: The Pod Modes Of Coherent Structuresmentioning

confidence: 99%

“…Thus, minimizing the Lagrangian Equation ( 15) must faithfully resolve a significant fraction of the subfilter-scale stress τ s ij . However, a sharp cutoff of frequencies does not translate into sharp cutoff of spatial scales [19,97]. Thus, we may better understand relatively difficult turbulent flows (e.g., [96,99]) by advancing the mixed-subgrid models that combine a temporal filtering approach with a spatially filtered subgrid model.…”

Section: The Pod Modes Of Coherent Structuresmentioning

confidence: 99%

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Wavelet Transforms and Machine Learning Methods for the Study of Turbulence

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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: The Filtered Navier-stokes Systemmentioning

confidence: 99%

Section: The Pod Modes Of Coherent Structuresmentioning

confidence: 99%

Section: The Pod Modes Of Coherent Structuresmentioning

confidence: 99%

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Wavelet Transforms and Machine Learning Methods for the Study of Turbulence

Alam

2023

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Advancing the temporal direct deconvolution method with spatial regularization

Oberle,

Pruett,

Jenny

2024

Physics of Fluids

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This study continues the exploration of temporal large-eddy simulation, particularly the extension of the temporal direct deconvolution method (TDDM) with a regularization term based on spatial dissipation. Furthermore, we aim to put insight stemming from previous work to test. Specifically, the hypothesis is that the temporal residual-stress leads to a reduction of the required artificial dissipation in under-resolved simulations. Moreover, this work seeks corroborate earlier discoveries with a posteriori results. We perform a numerical examination of two different spatial regularization terms in conjunction with TDDM: a spatial variant of selective frequency damping, functioning as a relaxation term that gradually drifts the velocity toward the filtered velocity, and the dynamic Smagorinsky model incorporating a prefactor. We test various cases, including the Taylor–Green vortex flow with a Reynolds number of Re = 3000, forced homogeneous isotropic turbulence with Reλ=200, turbulent channel flow at Reτ=590, and the flow over a periodic hill with Re = 10 935. Additionally, we also analyze the various dissipation contributions in TDDM as well as their interrelations. We also discuss grid artifacts and energy budget errors using these to compare the different models. Our results confirm the hypothesis that residual-stress dissipation reduces the necessary artificial dissipation. Because of the numerical ill-conditioning of deconvolution, whether temporal or spatial, there are practical limitations in the size of the filter width. Due to these limitations, the impact remains relatively minor. The a posteriori results of the new spatial regularization term show it to be effective in eliminating energy from the high wavenumber range.

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Eddy viscosity enhanced temporal direct deconvolution model for temporal large-eddy simulation of turbulent channel flow

Fan,

Wang,

Yuan

et al. 2024

Physics of Fluids

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In this work, a novel eddy viscosity enhanced temporal direct deconvolution model (TDDM) is proposed for temporal large-eddy simulation (TLES) of turbulent channel flow at large filter widths. To improve the accuracy of the constant eddy viscosity (CEV) model, particularly in the near-wall region, a damping function is incorporated to refine its performance. Moreover, a spatial filtering strategy is introduced to reduce the aliasing errors associated with the computation of subfilter-scale (SFS) stress, thereby enhancing numerical stability. In the a posteriori study, the accuracy of the CEV model is assessed comprehensively by comparing the TLES results with corresponding temporally filtered direct numerical simulation data. The results demonstrate that the CEV-enhanced TDDM provides accurate predictions across various statistical properties of velocity, instantaneous flow structures, kinetic energy spectra, and SFS energy fluxes. The coefficient sensitivity analysis of the CEV model reveals that the model coefficient significantly influences low Reynolds number flows, while its impact on high Reynolds number flows is relatively small. TLES on coarse grids demonstrate that the CEV-enhanced TDDM exhibits strong robustness and accuracy at different grid resolutions. Additionally, the CEV-enhanced TDDM in high Reynolds number flows is stable and accurate at remarkably large filter widths.

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Effects of time-filtering the Navier–Stokes equations

Cited by 4 publications

References 21 publications

Wavelet Transforms and Machine Learning Methods for the Study of Turbulence

Wavelet Transforms and Machine Learning Methods for the Study of Turbulence

Advancing the temporal direct deconvolution method with spatial regularization

Eddy viscosity enhanced temporal direct deconvolution model for temporal large-eddy simulation of turbulent channel flow

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