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Publication List

Preprints for most of our publications are available on arXiv. Refer to:

Publication Highlights

Below are selected publications with a picture and a short summary, grouped according to research areas. Click the titles to follow papers on the publisher's website.

Data-Driven Turbulence Modeling

Reynolds Averaged Navier-Stokes Equations with Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned

Journal of Fluid Mechanics 869, 553-586, 2019
J.-L. Wu, H. Xiao, R. Sun, and Q. Wang

A small error in Reynolds stress can lead to large errors in the mean velocity when solving the RANS equations because of poor model conditioning.  We derive a local condition number as an indicator of conditioning and demonstrate that this number explains the error propagation from Reynolds stress to mean velocity with examples.

Physics-Informed Covariance Kernel for Model-Form Uncertainty Quantification with Application to Turbulent Flows

Computers and Fluids 193 (2019) 104292
J.-L. Wu, C. Michelén-Ströfer, and H. Xiao

We present a method to derive physically meaningful covariance structure for problems with model discrepancy described by unclosed PDEs. The method exploits the fundamental connection between PDEs and covariance structure. We applied this method to UQ in turbulence modeling. 

Turbulence modeling in the age of data

Annual Review of Fluid Mechanics 51, 357-377, 2019
K. Duraisamy*, G. Iaccarino*, and H. Xiao* 
[* Contributed equally]

PRF 2018 Machine Learning Scheme

We survey recent developments in bounding uncertainties in RANS models via physical constraints, in adopting statistical inference to characterize model coefficients and estimate discrepancy, and in using machine learning to improve turbulence models. A central perspective we advocated is that by exploiting foundational knowledge in turbulence modeling and physical constraints, data-driven approaches can yield useful predictive models.

Quantification of model uncertainty in RANS simulations: A review

Progress in Aerospace Sciences, In Press, 2019
H. Xiao* and P. Cinnella*  
[* Contributed equally.]

PRF 2018 Machine Learning Scheme

Model uncertainties are a major obstacle for the predictive capability of RANS simulations. We review recent literature on data-free (uncertainty propagation) and data-driven (statistical inference) approaches for quantifying and reducing model uncertainties in RANS simulations.

Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework

Physical Review Fluids 2, 073602, 2018
J.-L. Wu, H. Xiao, and E. G. Paterson

PRF 2018 Machine Learning Scheme

We present a comprehensive framework for augmenting turbulence models with physics-informed machine learning, illustrating a complete workflow from identification of input/output to prediction of mean velocities. The learned model has Galilean invariance and coordinate rotational invariance. This work improves upon Wang et al. 2017 (see below).

We show that the discrepancies in Reynolds-averaged Navier-Stokes (RANS) modeled Reynolds stresses can be explained by mean flow features. A physics-informed machine learning framework is proposed to improve the predictive capabilities of RANS models by leveraging existing direct numerical simulations databases.

Quantifying and reducing model-form uncertainties in Reynolds averaged Navier–Stokes equations: A data-driven, physics-informed Bayesian approach

Journal of Computational Physics, 324, 115-136, 2016
H. Xiao, J.-L. Wu, J.-X. Wang, R. Sun, and C. J. Roy

We show that the model-form uncertainty of RANS simulations can be quantified and reduced via a Bayesian framework. Sparse observation of mean flow velocity is incorporated via Bayesian inference to quantify and reduce the uncertainties associated with the RANS-modeled Reynolds stresses.

A Bayesian calibration–prediction method for reducing model-form uncertainties with application in RANS simulations

Flow, Turbulence and Combustion, vol. 97, pp. 761-786, 2016
J.-L. Wu, J.-X. Wang, and H. Xiao

We used sparse observations to quantify and reduce the model-form uncertainty in RANS simulations, and the discrepancies so obtained are used to improve the predictions in other closely related flows, e.g., those with moderate changes in Reynolds numbers and geometry configurations. 

A priori assessment of prediction confidence for data-driven turbulence modeling

Flow, Turbulence and Combustion, vol. 99, pp. 25-46, 2017
J.-L. Wu, J.-X. Wang, H. Xiao, and J. Ling

We show that the prediction confidence of machine-learning-assisted turbulence modeling can be assessed a priori by evaluating the closeness between the training flows and the test flow in feature space. Two metrics, Mahalanobis distance and kernel density estimation, are explored and compared.

Particle-Resolving Simulations of Sediment Transport

The development of a three-dimensional, massively parallel, and open-source CFD–DEM solver SediFoam is detailed. Building upon open-source solvers OpenFOAM and LAMMPS, the solver has been shown to have excellent accuracy and scalability.


Diffusion-based coarse graining in hybrid continuum–discrete solvers: Theoretical formulation and a priori tests

International Journal of Multiphase Flow, 77, 142-157, 2015
R. Sun and H. Xiao

We proposed a new coarse graining algorithm for CFD-DEM based on solving a transient diffusion equation. The method is equivalent to the statistical kernel method with a Gaussian kernel. It is straightforward to implement and conserves both mass and momentum.

Realistic representation of grain shapes in CFD-DEM simulations of sediment transport with a bonded-sphere approach

Advances in Water Resources, 107, 421-438, 2017.
R. Sun, H. Xiao and H. Sun

Grain shapes may have significant impact on the dune dynamics. We propose a  simple algorithm to discretize common sediment-grain shapes in CFD-DEM simulations. The method can represent the fluid-induced torque on particles of irregular shapes.