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Hypersonic flow conditions pose exceptional challenges for Reynolds-Averaged Navier-Stokes (RANS) turbulence modeling. Critical phenomena include compressibility effects, shock/turbulent boundary layer interactions, turbulence-chemistry…

Turbulence modeling is a classical approach to address the multiscale nature of fluid turbulence. Instead of resolving all scales of motion, which is currently mathematically and numerically intractable, reduced models that capture the…

Model extrapolation to unseen flow is one of the biggest challenges facing data-driven turbulence modeling, especially for models with high dimensional inputs that involve many flow features. In this study we review previous efforts on…

Machine-learning (ML) techniques provide a new and encouraging perspective for constructing turbulence models for Reynolds-averaged Navier--Stokes (RANS) simulations. In this study, an iterative ML-RANS computational framework is proposed…

This chapter provides an introduction to data-driven techniques for the development and calibration of closure models for the Reynolds-Averaged Navier--Stokes (RANS) equations. RANS models are the workhorse for engineering applications of…

In computational fluid dynamics simulations of industrial flows, models based on the Reynolds-averaged Navier--Stokes (RANS) equations are expected to play an important role in decades to come. However, model uncertainties are still a major…

Reynolds-Averaged Navier-Stokes (RANS) models are widely used for turbulent flow simulations due to their computational efficiency, but their accuracy strongly depends on the selected turbulence closure and may vary across the flow domain.…

Accurate prediction of pressure and velocity fluctuations in turbulent flows is essential for understanding flow-induced vibration and structural fatigue. This study investigates the role of turbulence model parameter uncertainty in such…

A machine-learned (ML) model is developed to enhance the accuracy of turbulence transport equations of Reynolds Averaged Navier Stokes (RANS) solver and applied for periodic hill test case, which involves complex flow regimes, such as…

The constants and functions in Reynolds-averaged Navier Stokes (RANS) turbulence models are coupled. Consequently, modifications of a RANS model often negatively impact its basic calibrations, which is why machine-learned augmentations are…

In operational weather models, the effects of turbulence in the atmospheric boundary layer (ABL) on the resolved flow are modeled using turbulence parameterizations. These parameterizations typically use a predetermined set of model…

Reynolds-averaged Navier-Stokes (RANS) equations are widely used in engineering turbulent flow simulations. However, RANS predictions may have large discrepancies due to the uncertainties in modeled Reynolds stresses. Recently, Wang et al.…

Predictive simulation of many complex flows requires moving beyond Reynolds-averaged Navier-Stokes (RANS) based models to representations resolving at least some scales of turbulence in at least some regions of the flow. To resolve…

While many existing machine learning studies have focused on augmenting Reynolds averaged Navier Stokes (RANS) turbulence models for steady or time averaged unsteady flows, this paper takes a first step toward extending such augmentation to…

This work presents a review and perspectives on recent developments in the use of machine learning (ML) to augment Reynolds-averaged Navier--Stokes (RANS) and Large Eddy Simulation (LES) models of turbulent flows. Different approaches of…

Reynolds-averaged Navier-Stokes simulations are still the main method to study complex flows in engineering. However, traditional turbulence models cannot accurately predict flow fields with separations. In such situation, machine learning…

In this article, we propose a data-driven methodology for combining the solutions of a set of competing turbulence models. The individual model predictions are linearly combined for providing an ensemble solution accompanied by estimates of…

With the rising of modern data science, data--driven turbulence modeling with the aid of machine learning algorithms is becoming a new promising field. Many approaches are able to achieve better Reynolds stress prediction, with much lower…

An interpretable, physics-consistent turbulence model correction framework, termed FISR-Equation Learner (EQL), is proposed by embedding equation learning directly into a Partial Differential Equations (PDE)-constrained field inversion…

Data-driven methods for improving turbulence modeling in Reynolds-Averaged Navier-Stokes (RANS) simulations have gained significant interest in the computational fluid dynamics community. Modern machine learning algorithms have opened up a…