Session T39: Tubulence: Large-Eddy Simulations

The closure problem in large-eddy simulation from the viewpoint of information

A common misconception in large-eddy simulation (LES) modeling is that the closure problem of determining the subfilter-stress tensor arises from introducing the filter operator. Interestingly, this is not entirely accurate. Instead, an information-theoretic formalism shows that the closure problem is a consequence of the loss of information introduced by the filter, rather than the action of filtering itself. In general, reduced-order modeling, such as in LES, can be posed as a problem related to the conservation of information, where models aim to preserve the maximum amount of relevant information from the original system. In the case of LES, the actual closure problem emerges from the application of irreversible filters and/or the coarse discretization of the governing equations, which entail a truncation of the number of degrees of freedom in the system. In those situations, the LES grid resolution is unable to represent the small scales (i.e., subgrid scales), which in turn entails a loss of information. In this talk, we discuss the role of conservation of information as a fundamental aspect of LES modeling.   

Numerical error of explicitly filtered large-eddy simulation for consistent data-driven modeling

Data-driven techniques have been widely adopted in subgrid-scale (SGS) modeling of large-eddy simulations (LES) and show promising performance in a priori tests. However, the application of the data-driven models to simulations in the a posteriori tests is not necessarily consistent with a priori results. The inconsistency is partially due to extra numerical terms when using filtered direct numerical simulation (DNS) data for training the LES SGS stress term.

We separate the contribution of the SGS modeling and the numerical terms in LES, where the numerical term is a combination of commutation error, discretization of operators, and resolution truncation. DNS data from forced isotropic turbulence will be used for analysis. We study the effect of explicit filtering on both the SGS stress and the numerical term. We show that explicit filtering is crucial for reducing the contribution of the numerical term, and thus, obtaining a consistent data-driven model.   

Consistent Subgrid-scale Model Development for Large-eddy Simulation with Data-driven Sparse Identification

This study aims to model the subgrid-scale (SGS) stress and numerical error terms for large-eddy simulations (LES) applied to forced isotropic turbulence. Training data for the SGS and numerical error terms are obtained using a hybrid approach combining direct numerical simulation (DNS) and LES, known as DNS-aided LES. The model utilizes sparse regression to represent the SGS term as a linear combination of invariant tensors. To enhance accuracy, a neural network is trained on the residuals, including the numerical error term, compensating for filtering, discretization, and commutation errors. Results from both a priori and a posteriori testing of the model are presented to validate its efficacy.   

Fidelity of numerical discretization for spectrally-optimized subgrid-scale closures

This study assesses the effects of numerical discretization on spectrally-optimal subgrid-scale (SGS) closures discovered using a wavelet optimization framework. Nabavi & Kim (J. Fluid Mech. 2024) proposed a framework that optimizes SGS closures containing unknown constants for spectral energy transfer. In large-eddy simulation, numerical errors are manifested as implicit SGS dissipation, exceeding modeled SGS dissipation at coarse grid resolution. This is particularly the case for discretization errors. This study examines how discretization errors affect the optimized model constants. Two types of discretization errors are assessed, namely those associated with discretizing the governing equations and wavelet energy fluxes. For forced homogeneous isotropic turbulence at Re_λ = 85, pseudospectral and 2nd-order finite difference discretizations are used to perform direct numerical simulation (DNS). In addition, spectral and 2nd-order finite difference discretizations are employed for wavelet analysis. The effects of wavelet flux discretization are substantial, but simulation discretization has no effects on the model constants. Spectral discretization using the top-hat filter is incompatible with the wavelet framework, whereas 2nd-order discretization produces physically consistent results.   

Examining the Artificial Bottleneck Effect in Large Eddy Simulations

In Navier-Stokes turbulence, a bottleneck effect in the energy cascade near the viscous cutoff causes an overshoot in the energy spectrum relative to Komogorov’s -5/3 power-law scaling. A similar spectral overshoot occurs in large-eddy simulations (LES) when an eddy viscosity model is used. It is not a viscous phenomenon, but rather is caused by error in the residual stress model. This artificial bottleneck effect in LES leads to an over-prediction of kinetic energy even if a reliable dynamic procedure is used to accurately capture the spectral decay at the cutoff length scale.

This work uses Stokes flow regularization (SFR) and kinetic energy considerations to create LES models exploring the artificial bottleneck effect. A posteriori tests in isotropic turbulence compare the models’ impact on this effect. A key strategy of mitigating the bottleneck effect is to introduce a nonlinear gradient component in the residual stress closure, forming a dynamic mixed model. This approach effectively captures the local structure of residual stresses, leading to better representation of energy cascade efficiencies.

Specifically, the mixed model produces vortex tube-like structures that closely resemble those observed in the filtered DNS, whereas the eddy viscosity model produces a significantly different flow structure characterized by more shear layer-like structures (i.e.,vortex sheets rather than vortex tubes). The shear layers produced by the eddy viscosity models may be linked to the inverse cascade vortex thinning mechanism observed in 2D turbulence, suggesting a possible connection between the (artificial) bottleneck effect in 3D turbulence and the inverse cascade in 2D turbulence.   

Impact of Rib Spacing on Secondary Flows and Near-Wall Turbulence in Channel Flow: Insights from Large Eddy Simulation (LES)

This study employs Large Eddy Simulation (LES) to investigate secondary flows and near-wall turbulence, brought about by the surface-mounted longitudinal triangular ribs in a channel flow at a Reynolds number of 220, based on the channel height H and friction velocity. The rib aspect ratio has been taken as 2, with rib height as 0.1H. Two different rib spacings, such as 0.3H (low rib spacing) and 0.6H (high rib spacing) have been considered. The spanwise domain size has been taken as 3.6H, including 12 ribs for 0.3H spacing and 6 ribs for 0.6H spacing. Results show two counter-rotating vortices between adjacent ribs in both cases. For the low rib spacing case, secondary velocity impact is concentrated near the wall. For the high rib spacing case, it extends towards the top wall. The roughness function is relatively high for the case of low rib spacing. Wall shear stress is relatively high at the mid-plane of the ribs as compared to the spacing between the ribs. Near the wall and below the rib, for the case of low rib spacing, relatively lower production and dissipation of turbulent kinetic energy and normal Reynolds stresses are observed. The converse is observed above the rib height. Normal Reynolds stress exhibits strong anisotropic behaviour near the wall for both the cases, overlapping above 0.4H. For the low rib spacing case, two production peaks are observed, while for the case of high rib spacing only one peak is identified. The ratio of production to dissipation is found close to unity in the log-law region for both the cases.   

Dynamic Modal Filtering for Turbulence Modeling in Spectral Element Method

The lack of numerical dissipation in high-order spectral element methods has led to the development of new methods to introduce artificial dissipation. These techniques can serve both shock capturing and turbulence modelling purposes. In this study, dynamic explicit modal filtering is introduced to isolate the effects of sub-grid scale motions in under-resolved turbulent regions and enable the large-eddy simulation of turbulent flows. This filtering detects under-resolved areas through the instantaneous comparison of the local Kolmogorov length scale and the average grid spacing, then directly dissipates the excess energy by applying a modal low-pass filter on flow variables. The individual elemental operations in spectral-element method provides modes individually for each element and the filtering is applied separately for each element. The filtering intensity for under-resolved elements is adjusted based on the intensity of turbulence and the degree of under-resolvedness. The proposed filtering methodology shows high efficiency for the simulation of several benchmark turbulent flows.   

Anisotropic Models of Energy Transfer to the Subgrid for LES of Anisotropic Turbulence

Most currently available LES subgrid models assume unresolved turbulence to be isotropic. They therefore represent the transfer of energy to subgrid scales as isotropic. However, in LES of complex turbulent flows, where LES resolution is necessarily coarse, this assumption is generally invalid. In this case, the anisotropy of the unresolved turbulence needs to be accounted for, and in particular, accurately representing the anisotropy of the energy transfer to the subgrid is a necessary condition for predicting the resolved Reynolds stress. Furthermore, the subgrid turbulence also makes a significant contribution to the Reynolds stress. A tensor eddy viscosity subgrid model is proposed that is formulated in terms of the second moment of the resolved velocity gradient tensor. This is a fourth-rank tensor that encodes the anisotropy of the subgrid turbulence and thus allows the effects of anisotropy to be represented. The model's performance is assessed using a statistical a priori analysis based on filtered DNS simulations of a wide variety of homogeneous anisotropic test cases created by anisotropically forcing homogeneous turbulence. These DNS data will also be compared to the results of preliminary LES using the proposed model to determine the a posteriori performance of the model.