# Turbulence Modeling in the Age of Data

@article{Duraisamy2019TurbulenceMI, title={Turbulence Modeling in the Age of Data}, author={Karthik Duraisamy and Gianluca Iaccarino and Heng Xiao}, journal={Annual Review of Fluid Mechanics}, year={2019} }

Data from experiments and direct simulations of turbulence have historically been used to calibrate simple engineering models such as those based on the Reynolds-averaged Navier–Stokes (RANS) equations. In the past few years, with the availability of large and diverse data sets, researchers have begun to explore methods to systematically inform turbulence models with data, with the goal of quantifying and reducing model uncertainties. This review surveys recent developments in bounding…

## 573 Citations

### Quantification of model uncertainty in RANS simulations: A review

- PhysicsProgress in Aerospace Sciences
- 2019

### Ensemble gradient for learning turbulence models from indirect observations

- Computer Science, Environmental Science
- 2021

This paper explores the use of an ensemble approximation of the sensitivities of the RANS equations in training data-driven turbulence models with indirect observations and discusses the benefits and limitations of the ensemble gradient approximation as compared to the adjoint equations.

### Bayesian Additive Regression Trees for data-driven RANS turbulence modelling

- Computer Science
- 2019

The introduction of uncertainty in the anisotropic Reynolds stress fields mainly provides an additional tool to estimate the accuracy of machine learning predictions in case of the BART-TB model, however, the mean predicted solution does not seem to be a direct improvement over the TBRF.

### Reynolds-Averaged Turbulence Modeling Using Deep Learning with Local Flow Features: An Empirical Approach

- Computer Science
- 2020

The case of a backward-facing step is formulated to demonstrate that not only can DNNs discover underlying correlation behind fluid data but also they can be implemented in RANS to predict flow characteristics without numerical stability issues.

### Iterative Framework of Machine-Learning Based Turbulence Modeling for Reynolds-Averaged Navier-Stokes Simulations

- Computer Science
- 2019

A framework of machine-learning (ML) based turbulence modeling for Reynolds-averaged Navier-Stokes (RANS) equations is developed to close the Reynolds stress term in the RANS equations, and a promising prediction capability of the developed model is indicated even if the model is trained only with the data of channel flows.

### Data Driven Physics Constrained Perturbations for Turbulence Model Uncertainty Estimation

- Computer ScienceAAAI Spring Symposium: MLPS
- 2021

A framework that utilizes data driven algorithms in conjunction with physics based constraints to generate reliable uncertainty estimates for turbulence models while ensuring that the solutions are physically permissible is outlined.

### Machine learning methods for turbulence modeling in subsonic flows around airfoils

- EngineeringPhysics of Fluids
- 2019

Reynolds-Averaged Navier-Stokes(RANS) method will still play a vital role in the following several decade in aerospace engineering. Although RANS models are widely used, empiricism and large…

### Data-Driven Augmentation of Turbulence Models with Physics-Informed Machine Learning

- Computer Science
- 2018

The present work demonstrates a systematic procedure to generate mean flow features based on the integrity basis for a set of mean flow tensors, and proposes using machine learning to predict linear and nonlinear parts of the Reynolds stress tensor separately.

### An Iterative Machine-Learning Framework for Turbulence Modeling in RANS

- Computer Science
- 2019

An iterative ML-RANS computational framework is proposed, that combines the ML algorithm and transport equations of a conventional turbulence model built on empirical knowledge to maintain a consistent procedure to obtain the input features for ML models in both the training and predicting stages.

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