Modeling the pressure-Hessian tensor using deep neural networks

Parashar, Nishant; Srinivasan, Balaji Vasan; Sinha, Sawan Suman

doi:10.1103/physrevfluids.5.114604

Cited by 18 publications

(15 citation statements)

References 43 publications

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“…Their model was tested for duct and wavy-wall flows. We have recently been able to see the extension of TBNN to various flow configurations and problem settings, e.g., channel flow at various Reynolds numbers [14], a cylindrical and inclined jet in crossflow [15], and the pressure-Hessian based closure [16]. For the application to LES, the idea to estimate finer (unresolved) scales from solved large-scale information has widely been accepted with the supervised machine learning, whose training data is prepared by direct numerical simulation (DNS) [17,18,19,20,21,22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

Inserting machine-learned virtual wall velocity for large-eddy simulation of turbulent channel flows

Moriya,

Fukami,

Nabae

et al. 2021

Preprint

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We propose a supervised-machine-learning-based wall model for coarse-grid wall-resolved largeeddy simulation (LES). Our consideration is made on LES of turbulent channel flows with a first grid point set relatively far from the wall (∼ 10 wall units), while still resolving the near-wall region, to present a new path to save the computational cost. Convolutional neural network (CNN) is utilized to estimate a virtual wall-surface velocity from x − z sectional fields near the wall, whose training data are generated by a direct numerical simulation (DNS) at Re τ = 180. The virtual wall-surface velocity is prepared with the extrapolation of the DNS data near the wall. This idea enables us to give a proper wall condition to correct a velocity gradient near the wall. The estimation ability of the model from near wall information is first investigated as a priori test. The estimated velocity fields by the present CNN model are in statistical agreement with the reference DNS data. The model trained in a priori test is then combined with the LES as a posteriori test. We find that the LES can successfully be augmented using the present model at both the friction Reynolds number Re τ = 180 used for training and the unseen Reynolds number Re τ = 360 even when the first grid point is located at 5 wall units off the wall. We also investigate the robustness of the present model for the choice of sub-grid scale model and the possibility of transfer learning in a local domain. The observations through the paper suggest that the present model is a promising tool for recovering the accuracy of LES with a coarse grid near the wall.

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Section: Introductionmentioning

confidence: 99%

Inserting machine-learned virtual wall velocity for large-eddy simulation of turbulent channel flows

Moriya,

Fukami,

Nabae

et al. 2021

Preprint

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“…The methodology used in many of the studies discussed till now uses large high fidelity datasets obtained from DNS or LES simulations (Parashar, Srinivasan, and Sinha 2020). This data is used to train and validate machine learning based models, that can vary from deep learning based models or ensembled meta-models.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of machine learning algorithms for predictive Reynolds stress transport modeling

Panda¹,

Warrior²

2021

Preprint

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The application machine learning (ML) algorithms to turbulence modeling has shown promise over the last few years, but their application has been restricted to eddy viscosity based closure approaches. In this article we discuss rationale for the application of machine learning with high-fidelity turbulence data to develop models at the level of Reynolds stress transport modeling. Based on these rationale we compare different machine learning algorithms to determine their efficacy and robustness at modeling the different transport processes in the Reynolds Stress Transport Equations. Those data driven algorithms include Random forests, gradient boosted trees and neural networks. The direct numerical simulation (DNS) data for flow in channels is used both as training and testing of the ML models. The optimal hyper-parameters of the ML algorithms are determined using Bayesian optimization. The efficacy of above mentioned algorithms is assessed in the modeling and prediction of the terms in the Reynolds stress transport equations. It was observed that all the three algorithms predict the turbulence parameters with acceptable level of accuracy. These ML models are then applied for prediction of the pressure strain correlation of flow cases that are different from the flows used for training, to assess their robustness and generalizability. This explores the assertion that ML based data driven turbulence models can overcome the modeling limitations associated with the traditional turbulence models and ML models trained with large amounts data with different classes of flows can predict flow field with reasonable accuracy for unknown flows with similar flow physics. In addition to this verification we carry out validation for the final ML models by assessing the importance of different input features for prediction.

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“…(3). Attempts have been made to improve this approximation, which otherwise results in a finite time blow up of the reduced model for HIT [21][22][23]; such attempts include a multi-scale model that regularizes the singularity and retains the geometrical properties of the QR-model [24]. Then we reduce the information in A ij and θ j to the smallest possible number of scalar quantities resulting in an autonomous system.…”

mentioning

confidence: 99%

“…This provides valuable information on the geometry of the flow structures, as the Q-R phase space is divided by the Vieillefosse tail into regions where the flow gradients display different local properties [20,26]. In spite of the agreements, we recall that the QR-model has multiple limitations as, e.g., in the QR-model trajectories in phase space diverge in finite time, a process that is arrested in real fluids by pressure gradients and dissipation [6,7,[21][22][23][24]. Equation ( 9) contains the QR-model in its first two 14) is shown by the solid line, and the projection of the fixed points in Eq.…”

mentioning

confidence: 99%

“…Such GIMs often arise and play a relevant role, e.g., in reduced models for field gradients in fluids [3][4][5][6][7][8][9]20], where the persistence of low dimensional structures in complex and out-of-equilibrium flows is in many cases associated with the GIMs' existence. In such models, an important problem is how to improve approximations for the treatment of the pressure Hessian [21][22][23][24], but treatment of systems with more degrees of freedom than HIT as often appear in more realistic flows also faces the problem of how to find invariant manifolds and to characterize phase space as the complexity of the reduced system increases [8,25,[27][28][29]. In this case, as well as for other ODEs with GIMs with algebraic expressions, the method presented here can be of some value.…”

mentioning

confidence: 99%

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Extraction of invariant manifolds and application to turbulence with a passive scalar

Sujovolsky,

Mininni

2021

Preprint

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The reduction of dimensionality of physical systems, specially in fluid dynamics, leads in many situations to nonlinear ordinary differential equations which have global invariant manifolds with algebraic expressions containing relevant physical information of the original system. We present a method to identify such manifolds, and we apply it to a reduced model for the Lagrangian evolution of field gradients in homogeneous and isotropic turbulence with a passive scalar.

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Modeling the pressure-Hessian tensor using deep neural networks

Cited by 18 publications

References 43 publications

Inserting machine-learned virtual wall velocity for large-eddy simulation of turbulent channel flows

Inserting machine-learned virtual wall velocity for large-eddy simulation of turbulent channel flows

Evaluation of machine learning algorithms for predictive Reynolds stress transport modeling

Extraction of invariant manifolds and application to turbulence with a passive scalar

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