Session R43: Turbulence: LES

An efficient mixed dynamic Smagorinsky/scale-similarity subgrid model

It is well known that scale-similarity models have a high correlation of the subgrid stresses with the true stresses in a priori tests but provide very little subgrid dissipation to be practically useful. On the other hand, eddy-viscosity models such as the dynamic Smagorinsky model predict the subgrid dissipation well but correlate poorly with true subgrid stresses. This has motivated the use of mixed subgrid models that appear to retain the benefits of both models. However, dynamic mixed models typically require two or more levels of test filtering beyond the baseline (often implicit) grid filter, which makes it computationally expensive and cumbersome to implement and has limited their use in production codes.  We propose an efficient mixed subgrid model with a single level of test filtering and evaluate its performance through a priori and a posteriori testing of canonical flows including decaying isotropic turbulence and turbulent plane channel flows.   

Large-Eddy Simulation Models with Analytically-Derived Dynamic Coefficients Using Stokes Flow Regularization

Large eddy simulations (LES) are commonly used for turbulent flows to save on computational cost compared to DNS that requires resolving the Kolmogorov scale. A common approach to LES modeling is obtained from the filtering theory. For example, popular "dynamic" models use the Germano identity to determine model coefficients on the fly with a test filter calculation. In this work, the LES theory is re-imagined using Stokes Flow Regularization (SFR), a physics-inspired coarsening procedure. As a first demonstration of SFR-based LES modeling, an alternative to the Germano identity is introduced which allows for a dynamic and local determination of model coefficients via pen-and-paper analysis, without the need for a test filter. This new dynamic procedure will be demonstrated to generate equilibrium and non-equilibrium eddy viscosity and mixed model closures for the residual stress tensor. The models are tested a posteriori using DNS data to demonstrate the efficacy of the SFR-based dynamic procedure and the range of performance based on the assumed model form and grid resolution.   

Optimizing subgrid-scale closure constants for spectral energy transfer in homogeneous turbulence

The inter-scale energy flux of turbulent flows is used to optimize subgrid-scale (SGS) models. Using a wavelet multiresolution framework, the spectral energy flux due to the triadic interactions is estimated given a nominal grid cutoff scale of large-eddy simulation (LES). For a prescribed algebraic SGS closure, its constant is optimized a priori so that the modeled SGS dissipation balances the inter-scale energy transfer. The formulation is tested for incompressible homogeneous isotropic turbulence. For one-parameter eddy-viscosity models, the Smagorinsky constant is obtained if a cutoff scale is in the inertial subrange, consistent to the theoretical prediction. A posteriori results show that the dynamic estimation of the Smagorinsky model constant is consistent to a priori optimization and the dynamic model is spectrally optimal if the LES grid resolves the inertial subrange. The optimization is also performed for a two-parameter Clark-type model and a four-parameter tensor-coefficient-based Smagorinsky model, describing the roles of the individual closure terms.   

Subgrid parameterizations of ocean mesoscale eddies based on Germano decomposition

Ocean models at intermediate resolution (1/4), which partially resolve mesoscale eddies, can be seen as Large eddy simulations (LES) of the primitive equations, in which the effect of unresolved eddies must be parameterized. In this work, we propose new subgrid models that are consistent with the physics of two-dimensional (2D) flows. We analyze subgrid fluxes in barotropic decaying turbulence using (Germano, 1986) decomposition. We show that Leonard and Cross stresses are responsible for the enstrophy dissipation, while the Reynolds stress is responsible for additional kinetic energy backscatter. We utilize these findings to propose a new model, consisting of three parts, that is compared to a baseline dynamic Smagorinsky model (DSM). The three-component model accurately simulates the spectral transfer of energy and enstrophy and improves the representation of kinetic energy (KE) spectrum, resolved KE and enstrophy decay in a posteriori experiments. The backscattering component of the new model (Reynolds stress) is implemented both in quasi-geostrophic and primitive equation ocean models and improves statistical characteristics, such as the vertical profile of eddy kinetic energy, meridional overturning circulation and cascades of kinetic and potential energy.   

An autonomous LES method using eddy viscosity derived from the subgrid-scale similarity model

A previously developed method for large eddy simulations (LESs), based on spectral eddy viscosity models, is generalized to the physical space representation. The method estimates the subgrid scale (SGS) energy transfer using a similarity-type expression for the SGS tensor obtained using Gaussian filtering of velocity fields advanced in LESs. Subsequently, following steps for the spectral space representation, the SGS transfer in the physical space is used to obtain a spatially varying eddy viscosity at each time step in LESs. The eddy viscosity is then employed to model the SGS stress tensor in the familiar Boussinesq form for use in LESs. The method is autonomous in a sense that the functional form of the eddy viscosity is not postulated but is computed at each time step without adjustable constants from the resolved LES fields. The method is tested in LES of isotropic turbulence at high Reynolds numbers where the inertial range dynamics is expected and for lower Reynolds number decaying turbulence under conditions of the classical Comte-Bellot and Corrsin experiments. In both cases the agreement with reference data is very good and the SGS transfer computed for the proposed eddy viscosity model is highly correlated with the transfer computed for the similarity model ($C approx 0.8$).   

An Efficient Data-Driven Closure Modeling Framework for Interpretable Sub-Grid Scale Stress Model Development Via Sparse Regression

Despite the projected advancements in computer speed and memory in the coming decades, high-fidelity, complex turbulent flow field simulations are fated intractable on average computers for the foreseeable future. This indicates the pressing need for new methodologies to build accurate turbulence closure models that use fewer computational resources. In recent years, data-driven approaches -- most popularly, neural networks -- have demonstrated promise for advancing the state-of-the-art in terms of predictive performance. Neural networks, however, suffer from a lack of interpretability due to their “black box” nature, which inevitably obscures the underlying physics and routinely increases the computational cost over that of conventional models. To address these issues, we propose a data-driven framework to discover explicit, algebraic, closed-form nonlinear eddy viscosity (NLEV) models of the sub-grid scale (SGS) stress tensor via sparse regression techniques. To embed invariance properties directly into the model form, training is performed over a minimal tensor basis that is scaled by a truncated infinite polynomial expansion of invariant scalars. We modulate model dissipation error by implementing a custom optimization function. Our SGS modeling framework also generalizes to anisotropic grids by using a mapping to the isotropic space. We demonstrate the robustness and efficiency of our NLEV model in both a priori and a posteriori tests.   

Numerically consistent data-driven subgrid-scale model for large-eddy simulation

In this work, we train a data-driven subgrid-scale (SGS) model for large-eddy simulation (LES) which incorporates numerical error arising from the LES equations. LES solves the low-pass filtered Navier-Stokes equations while using a model for unclosed SGS terms. The typical approach for generating data-driven closure models in LES computes required SGS terms using a filtering operator on direct numerical simulation (DNS) data. Recent research highlights that the numerical error between the derivative and filter operators is comparable to the modeling error of traditional SGS models. We develop an artificial neural network (ANN) trained on both filtered DNS data and computed commutation error to act as a numerically consistent closure model in LES. Our goal is to create a high fidelity SGS model for LES which can adapt to different numerical methods in computational fluid dynamics solvers. The results of this ANN-augmented LES model are evaluated in the case of forced isotropic turbulence.   

Tensor Networks for Solving the PDF/FDF Transport

 

The PDF-FDF methodologies have proven very effective for RANS-LES of chemically reactive turbulent flows.  Due to their inherent capabilities, the equations governing the transport of PDF/FDF are high dimensional. It is shown that  “tensor networks”  (TN) can deal with such a large dimensional transport in a very effective manner.  These networks are employed here to tackle the Fokker-Planck form of the PDF/FDF instead of the Langevin form as is typically done via Monte Carlo methodologies. Demonstrative simulations are conducted of a  chemically reactive flow, governed by a time-dependent five-dimensional  modelled Fokker-Planck equation.