Subgrid-scale Stress Research Articles

Large-eddy simulation of tip clearance cavitating flow around a hydrofoil

Large-eddy simulations of tip clearance cavitating flow between a National Advisory Committee for Aeronautics 0012 hydrofoil and the endwall have been performed to investigate the effects of cavitation on vortical structures, turbulence statistics and hydrofoil performance within the tip clearance region. The wall-adapting local eddy-viscosity model is employed to compute the subgrid-scale stress, and the Zwart-Gerber-Belamri cavitation model is used to predict the cavitating flow. The simulation results show that cavitation has insignificant effects on the tip clearance flow structures and the wandering motion of the tip leakage vortex (TLV). Detailed analysis of turbulence statistics indicates that the turbulent kinetic energy and pressure fluctuation inside the TLV core are significantly increased under the effect of cavitation. In addition, it is found that cavitation enhances the unstable wall-normal motion of the TLV, leading to the enhancement of turbulence near the TLV core. The hydrofoil performance affected by cavitation is also investigated, showing that the lift and drag forces acting on the hydrofoil is substantially reduced due to the cavitation.

Subgrid-scale model considering the inverse energy cascade using an artificial neural network

For the closure of the subgrid-scale (SGS) stress tensor, an artificial neural network (ANN)-based SGS model that takes account of the inverse energy cascade in isotropic turbulence is developed. The data required for training this ANN-based SGS model are provided by direct numerical simulation of isotropic turbulence with an inverse energy cascade. Two input features, the root mean square of the rate-of-strain tensor and the product of the eigenvalues of the rate-of-strain tensor, are employed to characterize the inverse energy cascade. An a priori test reveals that the ANN-based model adequately predicts the SGS stress tensor in the backward energy transfer process, and the predictive capability of the gradient model is found to be slightly poorer than that of the ANN-based model, while that of the Smagorinsky model is not satisfactory. In comparison with the gradient model, the ANN-based model even predicts a few backward energy transfer events in the stage of excessive energy dissipation. In addition, the off-diagonal component of the SGS stress tensor, rather than the diagonal component, may be intimately associated with the inverse energy cascade. The ANN-based SGS model presented here is expected to provide inspiration for future investigations of the construction of SGS models that take account of the inverse energy cascade.

A transformer-based convolutional method to model inverse cascade in forced two-dimensional turbulence

The present work proposes a novel transformer-based convolutional neural network (TransCNN) method to effectively model the inverse energy cascade in two dimensional (2D) turbulence. The TransCNN structure combines large-scale features extracted by transformer with small-scale features from convolutional layers, thus is considered suitable for multi-scale modeling. The novel TransCNN method has been applied to model sub-grid scale (SGS) stress for large-eddy simulation (LES) of 2D turbulence, under the extremely challenging situation that the LES grid is too coarse to resolve the external forcing scale. The data-driven model trained by the novel TransCNN structure is compared to two deep CNN models with varying complexities. All models exhibit proficiency during a priori tests. Notably, TransCNN surpasses its counterparts in predictive accuracy and generalizability in a posteriori tests. An investigation into the receptive fields reveals that the TransCNN model can efficiently leverage global information with the transformer structure, which is key to its superior performance in representing the inverse energy cascade in the 2D turbulent simulations.

A novel subgrid-scale stress model considering the influence of combustion on turbulence: A priori and a posteriori assessment

Most classical turbulence models were proposed and developed based on non-reacting flows without considering the effects of combustion on turbulence. The flow structure in turbulent combustion is more complex, creating challenges to the applicability of traditional turbulence models. Given this, a novel flame surface and k-equation-based gradient model (FKGM) considering combustion effects is proposed for the modeling of the subgrid-scale (SGS) stress in large eddy simulation (LES). The SGS stress is calculated based on the SGS kinetic energy (kSGS) and normalized velocity gradient. The velocity gradient incorporates first-order gradients at multiple stencil locations and considers the anisotropy of the stress near the flame surface. The FKGM model is first validated by the a priori analysis based on the direct numerical simulation (DNS) database of a premixed swirling flame. The closure terms of the kSGS equation are well validated, and the predicted SGS stress using the FKGM model achieves good agreement with the filtered DNS results. In the a posteriori LES study, the FKGM model demonstrates better performance compared with the traditional dynamic Smagorinsky model and velocity gradient model, providing more accurate predictions for mean and fluctuation velocities. The error analysis for SGS kinetic energy is further conducted by comparing the LES results with the DNS data, and the results indicate that the underestimation of the generation term of the kSGS equation is the main source of error.

Artificial neural-network-based subgrid-scale model for large-eddy simulation of isotropic turbulence

This study is concerned with accurately predicting the subgrid-scale (SGS) stress using an artificial neural network (ANN) with a linear eddy-viscosity term and a nonlinear term as the input variables. A priori and a posteriori tests are conducted to examine the prediction performance of the ANN-based SGS stress model in decaying homogeneous isotropic turbulence. In a priori test, the present ANN-based SGS model shows high correlation coefficients between the true and predicted SGS stresses, and excellent predictions of the SGS stress and dissipation. In a posteriori test, it is found that the ANN-based SGS model can predict the turbulence statistics more accurately than the traditional dynamic SGS models. The generalization capabilities of the model to untrained flow conditions and unstrained types of turbulent flow have been evaluated. It is found that the proposed ANN-based model can provide an accurate prediction of the SGS stress under different Reynolds numbers and flow types. A comparison among several existing ANN-based models with different input variables is presented, demonstrating a significant advantage of the present model.

A thermodynamic computational model analysis of a newly designed Tri-Rotor (T-R) volume air compressor

A thermodynamic computational modelling (TCM) approach is developed to model and simulate thermodynamic processes of a newly designed rotary type air compressor named ‘tri-rotor (T-R) compressor’ using a Lattice-Boltzmann Method (LBM) based fluid flow solution, which is applied for the first time to a rotary compressor flow. With this method, which is combined with a Wall-Adapting Local Eddy-viscosity sub-grid scale stress (SGS) model (WALE), time-consuming classic fluid-domain meshing/re-meshing process is not required and a mesh deformation problem leading to numerical instability is overcome by generating a fixed Cartesian lattice. The proposed TCM approach here is expected to serve as a basis for transient simulations of rotating turbulent and highly compressible flow for accurate and more complete computational representation of an ideal, adiabatic compression process through pressure − rotational angle (P-Theta degree) and volume − rotational angle (V-Theta degree) diagrams. The designed compressor is comprised of three specifically shaped, simultaneously rotating rotors, which are well-positioned in a cylinder to draw and discharge air uninterruptedly through two-suction and two-discharge ports, respectively and achieves higher mass-flow rates with increasing rotational speed. A comparative study with different rotational speeds predicts that high isentropic efficiency ranging from 0.850 to 0.941 can be attained for the investigated rotational speed range without any compromise on mass flow rates and pressure ratios. A proof-of-concept experiment of a full-scale T-R compressor model is conducted to assess its operational feasibility and performance. It is found that the TCM approach reproduces comparable results to those obtained from the preliminary experimental studies.

Autonomous large-eddy simulations of turbulence using eddy viscosity derived from the subgrid-scale similarity stress tensor

A previously developed method for large-eddy simulations (LES), based on spectral eddy-viscosity models, is generalised to the physical space representation. The method estimates the subgrid-scale (SGS) energy transfer using a similarity-type model expression for the SGS tensor obtained using Gaussian filtering of velocity fields advanced in the simulations. 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 LES. The computed eddy viscosity is employed to model the SGS stress tensor in the familiar Boussinesq form for use in LES. 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-type stress tensor.

A-priori evaluation of data-driven models for large-eddy simulations in Rayleigh–Bénard convection

Natural convection is a commonly occurring heat-transfer problem in many industrial flows and its prediction with conventional large eddy simulations (LES) at higher Rayleigh numbers using progressively coarser grids leads to increasingly inaccurate estimates of important performance indicators, such as Nusselt number (Nu). Thus, to improve the heat transfer predictions, we utilize Gene Expression Programming (GEP) to develop sub-grid scale (SGS) stress and SGS heat-flux models simultaneously for LES. The models’ development is performed using reference direct numerical simulation data of a typical natural convection case, i.e. the Rayleigh–Bénard convection (RBC). The training frameworks are built by using alignment as the evaluation metrics of the basis functions when comparing to the Gaussian-filtered SGS stress and SGS heat-flux. The trained models in isotropic form, by utilizing the L2 norm of the grid cell ΔL2 as the length scale, demonstrate good performance in the bulk region, but less improved performance in the near wall region. It is shown, that for LES of wall-bounded flow, the GEP models in anisotropic form, i.e. using different grid length scale for the different spatial directions, are required to obtain generalized models suitable for different regions. Consequently, the a-priori results demonstrate a significant improvement in the prediction of both instantaneous and mean quantities for a wide range of filter widths.

Turbulence Closure With Small, Local Neural Networks: Forced Two‐Dimensional and β‐Plane Flows

AbstractWe parameterize sub‐grid scale (SGS) fluxes in sinusoidally forced two‐dimensional turbulence on the β‐plane at high Reynolds numbers (Re ∼25,000) using simple 2‐layer convolutional neural networks (CNN) having only O(1000) parameters, two orders of magnitude smaller than recent studies employing deeper CNNs with 8–10 layers; we obtain stable, accurate, and long‐term online or a posteriori solutions at 16× downscaling factors. Our methodology significantly improves training efficiency and speed of online large eddy simulations runs, while offering insights into the physics of closure in such turbulent flows. Our approach benefits from extensive hyperparameter searching in learning rate and weight decay coefficient space, as well as the use of cyclical learning rate annealing, which leads to more robust and accurate online solutions compared to fixed learning rates. Our CNNs use either the coarse velocity or the vorticity and strain fields as inputs, and output the two components of the deviatoric stress tensor, Sd. We minimize a loss between the SGS vorticity flux divergence (computed from the high‐resolution solver) and that obtained from the CNN‐modeled Sd, without requiring energy or enstrophy preserving constraints. The success of shallow CNNs in accurately parameterizing this class of turbulent flows implies that the SGS stresses have a weak non‐local dependence on coarse fields; it also aligns with our physical conception that small‐scales are locally controlled by larger scales such as vortices and their strained filaments. Furthermore, 2‐layer CNN‐parameterizations are more likely to be interpretable.

Large eddy simulations of turbulent pipe flows at moderate Reynolds numbers

Wall-bounded turbulence is relevant for many engineering and natural science applications, yet there are still aspects of its underlying physics that are not fully understood, particularly at high Reynolds numbers. In this study, we investigate fully developed turbulent pipe flows at moderate-to-high friction velocity Reynolds numbers (361≤Reτ≤2000), corresponding to bulk velocity-based Reynolds numbers of 11 700≤Reb≤82 500, using wall-modeled large eddy simulations (LES) in OpenFOAM. A grid convergence study is performed for Reτ=361, followed by an investigation of the accuracy of various subgrid-scale stress models for the same Reynolds number. Results show that the wall-adapting local eddy (WALE) model performs well compared to experiments and direct numerical simulations, while one-equation eddy-viscosity model and Smagorinsky are too dissipative. LES utilizing WALE is then performed for four different Reynolds numbers with gradually refined grids, revealing excellent agreement with DNS data in the outer region. However, a significant deviation from DNS data is observed in the sub-viscous layer region, indicating the need for further mesh refinement in the wall-normal direction to accurately capture the smallest-scale motions' behavior. Additional mesh sensitivity analysis uncovered that, as the Reτ value rises, it becomes crucial for a grid to adhere to the condition of Δx+≤20−25 and Δz+≤10 in order to precisely capture substantial large and small-scale fluctuations. Overall, the WALE model enables accurate numerical simulations of high-Reynolds number, wall-bounded flows at a fraction of the computational cost required for temporal and spatial resolution of the inner layer.

Large eddy simulation of flow over a circular cylinder with a neural-network-based subgrid-scale model

A neural-network-based large eddy simulation is performed for flow over a circular cylinder. To predict the subgrid-scale (SGS) stresses, we train two fully connected neural network (FCNN) architectures with and without fusing information from two separate single-frame networks (FU and nFU, respectively), where the input variable is either the strain rate (SR) or the velocity gradient (VG). As the input variables, only the grid-filtered variables are considered for the SGS models of G-SR and G-VG, and both the grid- and test-filtered variables are considered for the SGS models of T-SR and T-VG. The training data are the filtered direct numerical simulation (fDNS) data at $Re_d=3900$ based on the free-stream velocity and cylinder diameter. Using the same grid resolution as that of the training data, the performances of G-SR and G-VG (grid-filtered inputs) and T-SR-FU and T-VG-FU (grid- and test-filtered inputs with fusion) are better than those of the dynamic Smagorinsky model and T-SR-nFU and T-VG-nFU (grid- and test-filtered inputs without fusion). These FCNN-based SGS models are applied to untrained flows having different grid resolutions from that of training data. Although the performances of G-SR and G-VG are degraded, T-SR-FU and T-VG-FU still provide good performances. Finally, T-SR-FU and T-VG-FU trained at $Re_d = 3900$ are applied to higher-Reynolds-number flows ( $Re_d = 5000$ and 10 000) and their results are also in good agreements with those of fDNS and previous experiment, indicating that adding the test-filtered variables and fusion increases the prediction capability even for untrained Reynolds number flows.

Invariance embedded physics-infused deep neural network-based sub-grid scale models for turbulent flows

In this paper, we present two novel physics-infused neural network (NN) architectures that satisfy various invariance conditions for constructing efficient and robust Deep Learning (DL)-based sub-grid scale (SGS) turbulence models for use in Large Eddy Simulation (LES) procedures widely used in various fluid engineering applications. The first architecture, called tensor basis neural networks (TBNN), recently proposed in the context of Reynolds-averaged Navier–Stokes (RANS) modeling, and introduced herein for SGS modeling of wall-bounded turbulence, embeds the analytical expansion of the SGS turbulence stresses into integrity basis tensors composed of the symmetric and anti-symmetric parts of the resolved velocity gradient tensor, thus incorporating the Galilean, rotational and reflectional invariances. In our second approach, a relatively simple yet powerful architecture, called Galilean Invariance embedded Neural Network (GINN) incorporates the Galilean invariance, and takes in as inputs the independent components of the integrity basis tensors in addition to the invariant inputs in a single input layer. Explicit filtering of data from direct simulations of the canonical channel flow at two friction Reynolds numbers Reτ≈395 and 590 provided accurate data for training and testing these models. Both sets of models are used to predict the SGS stresses for feature datasets generated with different filter widths, and at different Reynolds numbers. The GINN model yields less prediction error on test datasets (mean squared error ∼0.4) compared to the TBNN model (mean squared error ∼0.5). Upon comparison, it is revealed that GINN has better feature extraction capacity owing to its ability to establish relations between and extract information from cross-components of the integrity basis tensors and the SGS stresses. Based on their predictive performance, both models proposed herein have shown great promise for use in a posteriori actual LESs. The present work illustrates the significance of physics infusion as well as invariance embedding into NN architecture for constructing efficient and robust DL-based SGS turbulent models in achieving superior predictive efficacy.

A priori test of Large-Eddy Simulation models for the Sub-Grid Scale turbulent stress tensor in perfect and transcritical compressible real gas Homogeneous Isotropic Turbulence

In this study, the focus lies on the modeling of the subgrid-scale stress tensor in the context of real gas flows. By conducting tests on perfect and dense gas configurations using six different models, the research findings highlight the superiority of gradient models over eddy-viscosity models in capturing the structural behavior of the stress tensor. However, the models’ performance experiences a significant decline when considering the intricate thermodynamics of real gases. To address this challenge, dynamic models that take into account the characteristics of the flow are also tested, resulting in some improvements in the outcomes. Despite these advancements, the achieved results still fall short of being entirely satisfactory. In particular, the models fail to accurately predict the occurrence of large values of the subgrid-scale stress tensor in the real gas flow. The complex thermodynamic nature of real gases therefore significantly influences the subgrid-scale stress tensor and the outcomes of this study underscore the urgent need for continued research to advance our understanding and modeling capabilities of subgrid-scale terms in real gas flows, paving the way for statistically accurate Large-Eddy Simulations of industrial real gas flows using moderately refined grids.

Ensemble data assimilation-based mixed subgrid-scale model for large-eddy simulations

An ensemble Kalman filter (EnKF)-based mixed model (EnKF-MM) is proposed for the subgrid-scale (SGS) closure in the large-eddy simulation (LES) of turbulence. The model coefficients are determined through the EnKF-based data assimilation technique. The direct numerical simulation (DNS) results are filtered to obtain the benchmark data for the LES. Reconstructing the correct kinetic energy spectrum of the filtered DNS (fDNS) data has been adopted as the target for the EnKF to optimize the coefficient of the functional part in the mixed model. The proposed EnKF-MM framework is subsequently tested in the LES of both the incompressible homogeneous isotropic turbulence and turbulent mixing layer. The performance of the LES is comprehensively examined through the predictions of the flow statistics including the velocity spectrum, the probability density functions (PDFs) of the SGS stress, the PDF of the strain rate, and the PDF of the SGS energy flux. The structure functions, the evolution of turbulent kinetic energy, the mean flow, the Reynolds stress profile, and the iso-surface of the Q-criterion are also examined to evaluate the spatial–temporal predictions by different SGS models. The results of the EnKF-MM framework are consistently more satisfying compared to the traditional SGS models, including the dynamic Smagorinsky model, the dynamic mixed model, and the velocity gradient model, demonstrating its great potential in the optimization of SGS models for the LES of turbulence.

Unsteady flow enhancement on an airfoil using sliding window weak-constraint four-dimensional variational data assimilation

This study establishes a continuous sliding window weak-constraint four-dimensional variational approach for reproducing a complete instantaneous flow from sparse spatiotemporal velocity observations. The initial condition, boundary condition, and model-form uncertainties are corrected simultaneously by a spatiotemporally varying additive forcing, coupled with the large eddy simulation (LES) framework, which reinforces subgrid-scale viscosity stresses and simplifies gradient computation. The additive force undergoes a Stokes–Helmholtz decomposition to ensure divergence-free projection and natural pressure determination. The model is theoretically derived to minimize discrepancies between the sparse velocity observations and the numerical predictions of the primary-adjoint system, enabling optimal contribution of the additive force. Synthetic data from a fine-grid LES of the vortical flow over an NACA0012 airfoil are used as observations. The algorithm is evaluated on a benchmark case, where observations are subsampled at 1/400 000 spatiotemporal resolution required for an LES. The sliding window strategy expands the dependence domain of the observations and mitigates the impact of primary-adjoint chaos, achieving over 90% pointwise correlation for filtered parameters and 80% spectral correlation for all of the resolved wavenumbers. Despite the lack of near-wall observations, streaks are accurately recovered due to the convective sensitivity of the observations from the outer flow. While the pressure fluctuation in the inflow region is not as well excited as in LES, recovery is augmented downstream. In both the inner and outer wall layers, the pressure distributions are obtained reasonably well by capturing the signatures of the vortical structure and their downstream convection. The robustness of the algorithm to observation noise is demonstrated. Finally, the impact of temporal resolution on estimation is evaluated, establishing a resolution threshold for successful reconstruction.

Neural-network-based mixed subgrid-scale model for turbulent flow

An artificial neural-network-based subgrid-scale (SGS) model, which is capable of predicting turbulent flows at untrained Reynolds numbers and on untrained grid resolution is developed. Providing the grid-scale strain-rate tensor alone as an input leads the model to predict a SGS stress tensor that aligns with the strain-rate tensor, and the model performs similarly to the dynamic Smagorinsky model. On the other hand, providing the resolved stress tensor as an input in addition to the strain-rate tensor is found to significantly improve the prediction of the SGS stress and dissipation, and thereby the accuracy and stability of the solution. In an attempt to apply the neural-network-based model trained for turbulent flows with a limited range of the Reynolds number and grid resolution to turbulent flows at untrained conditions on untrained grid resolution, special attention is given to the normalisation of the input and output tensors. It is found that the successful generalization of the model to turbulence for various untrained conditions and resolution is possible if distributions of the normalised inputs and outputs of the neural network remain unchanged as the Reynolds number and grid resolution vary. In a posteriori tests of the forced and the decaying homogeneous isotropic turbulence and turbulent channel flows, the developed neural-network model is found to predict turbulence statistics more accurately, maintain the numerical stability without ad hoc stabilisation such as clipping of the excessive backscatter, and to be computationally more efficient than the algebraic dynamic SGS models.

Quantifying 3D Gravity Wave Drag in a Library of Tropical Convection‐Permitting Simulations for Data‐Driven Parameterizations

AbstractAtmospheric gravity waves (GWs) span a broad range of length scales. As a result, the un‐resolved and under‐resolved GWs have to be represented using a sub‐grid scale (SGS) parameterization in general circulation models (GCMs). In recent years, machine learning (ML) techniques have emerged as novel methods for SGS modeling of climate processes. In the widely used approach of supervised (offline) learning, the true representation of the SGS terms have to be properly extracted from high‐fidelity data (e.g., GW‐resolving simulations). However, this is a non‐trivial task, and the quality of the ML‐based parameterization significantly hinges on the quality of these SGS terms. Here, we compare three methods to extract 3D GW fluxes and the resulting drag (Gravity Wave Drag [GWD]) from high‐resolution simulations: Helmholtz decomposition, and spatial filtering to compute the Reynolds stress and the full SGS stress. In addition to previous studies that focused only on vertical fluxes by GWs, we also quantify the SGS GWD due to lateral momentum fluxes. We build and utilize a library of tropical high‐resolution (Δx = 3 km) simulations using weather research and forecasting model. Results show that the SGS lateral momentum fluxes could have a significant contribution to the total GWD. Moreover, when estimating GWD due to lateral effects, interactions between the SGS and the resolved large‐scale flow need to be considered. The sensitivity of the results to different filter type and length scale (dependent on GCM resolution) is also explored to inform the scale‐awareness in the development of data‐driven parameterizations.

Non-equilibrium extension of the explicit algebraic subgrid-scale stress model with application to turbulent channel flow at low Reynolds numbers

An extension of the explicit algebraic subgrid-scale (SGS) stress model (EASSM) of Marstorp et al. [J. Fluid Mech. 639, 403–432 (2009)] is proposed to account for the non-local equilibrium between the production, P, and viscous dissipation, ϵ, of the SGS turbulent kinetic energy in its formulation. The original derivation of the EASSM uses the equilibrium assumption P=ϵ, whereas in the current new derivation, a cubic algebraic equation is extracted for P/ϵ from the modeled transport equation for the SGS stress anisotropy, which can be solved to improve the EASSM predictions with less than 4% additional computational costs per time step. The performance of the extended EASSM is assessed in large-eddy simulation of plane turbulent channel flow at Reτ=587 and 179 for a wide range of resolutions, where deviations from the local equilibrium assumption are expected at the vicinity of the walls. The enhanced EASSM formulation lowers resolution dependence of the model predictions and improves its predictions at low resolutions. The improvements affected major one-point turbulence statistics of interest, such as the wall shear stress, mean velocity, Reynolds stresses, and SGS dissipation as well as the two-point velocity correlations and premultiplied spanwise spectra of the streamwise velocity. The predicted mean P/ϵ also reasonably agrees with the filtered direct numerical simulation data.

Scale-to-scale energy transfer in rarefaction-driven Rayleigh–Taylor instability-induced transitional mixing

The rarefaction-driven Rayleigh–Taylor instability-induced mixing flow is numerically investigated via large eddy simulation. Prior analyses of interfacial diffusion are conducted to clarify the scale-to-scale transfer of kinetic energy during the laminar-to-turbulent transition. The statistical characteristics, including subgrid-scale (SGS) turbulent kinetic energy and SGS stresses, are outlined and highlight the mechanical production as well as pressure-related effects. Further inspection reveals that the relative intensity of SGS backscatter is somewhat noticeable, particularly for the transition onset, and the large-scale pressure-dilatation work is regulated through volumetric compression and expansion. Joint probability density function and the conditional averaging approaches both manifest that SGS backscatter is extremely associated with properties of the surrounding flow expansion induced by quadrupolar vortex structures. Furthermore, investigations on the effects of SGS backscatter on eddy viscosity are performed, and a regime classification, illustrating the relationship between various energy conversion modes and signs of the eddy viscosity, is provided. It is found that there is a significantly strong correlation between SGS backscatter and negative eddy viscosity; meanwhile, the volumetric compression and expansion tend to modulate the scale-to-scale energy transfer throughout the transitional process.

Exploration of robust machine learning strategy for subgrid scale stress modeling

Various aspects of machine learning (ML) are explored to resolve limitations appearing in current ML-based subgrid scale (SGS) stress modeling. Graph neural network (GNN), applied in the present study, allows flexible and rigorous use of spatial convolution regardless of the proximity to physical boundaries and mesh uniformity. Along with GNN, the proposed feature scaling method relies only on the local quantities and can be applied for a range of flow configurations. A data augmentation method is also proposed to consider the rotational invariant. All these techniques are implemented in the present model, and the model is compared with versions of corresponding ML-based models including a typical multilayer perceptron (MLP) for various flow configurations. The results showed that both GNN and MLP models yield reasonable prediction overall. However, GNN shows superior performance near-wall due to spatial convolution. Although the present method implements the rotational invariant discretely, the augmentation method is found to produce consistent performance for any rotated coordinates. The minimal flow configuration, which can train a model to predict a range of flow configurations, is also explored. It is found that a model trained based on turbulent channel flows alone yields a close level of prediction robustness to the ones trained with multiple flow configurations. The developed GNN model is implemented in OpenFOAM, and large eddy simulation (LES) results are compared with corresponding direct numerical simulation data. With these proposed techniques, ML-based SGS models can be improved in terms of robustness and usability for a range of LES applications.