Imperial College London
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ProfessorSylvainLaizet

Faculty of Engineering, Department of Aeronautics

Professor in Computational Fluid Mechanics
 
 
 
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Contact

 

+44 (0)20 7594 5045s.laizet Website

 
 
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Location

 

339City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Wu:2019:10.1016/j.cma.2018.09.010,
author = {Wu, J and Sun, R and Laizet, S and Xiao, H},
doi = {10.1016/j.cma.2018.09.010},
journal = {Computer Methods in Applied Mechanics and Engineering},
pages = {707--726},
title = {Representation of stress tensor perturbations with application in machine-learning-assisted turbulence modeling},
url = {http://dx.doi.org/10.1016/j.cma.2018.09.010},
volume = {346},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Numerical simulations based on Reynolds-Averaged Navier–Stokes (RANS) equations are widely used in engineering design and analysis involving turbulent flows. However, RANS simulations are known to be unreliable in many flows of engineering relevance, which is largely caused by model-form uncertainties associated with the Reynolds stresses. Recently, a machine-learning approach has been proposed to quantify the discrepancies between RANS modeled Reynolds stress and the true Reynolds stress. However, it remains a challenge to represent discrepancies in the Reynolds stress eigenvectors in machine learning due to the requirements of spatial smoothness, frame-independence, and realizability. This challenge also exists in the data-driven computational mechanics in general where quantifying the perturbation of stress tensors is needed. In this work, we propose three schemes for representing perturbations to the eigenvectors of RANS modeled Reynolds stresses: (1) discrepancy-based Euler angles, (2) direct-rotation-based Euler angles, and (3) unit quaternions. We compare these metrics by performing a priori and a posteriori tests on two canonical flows: fully developed turbulent flows in a square duct and massively separated flows over periodic hills. The results demonstrate that the direct-rotation-based Euler angles representation lacks spatial smoothness while the discrepancy-based Euler angles representation lacks frame-independence, making them unsuitable for being used in machine-learning-assisted turbulence modeling. In contrast, the representation based on unit quaternion satisfies all the requirements stated above, and thus it is an ideal choice in representing the perturbations associated with the eigenvectors of Reynolds stress tensors. This finding has clear importance for uncertainty quantification and machine learning in turbulence modeling and for data-driven computational mechanics in general.
AU  - Wu,J
AU  - Sun,R
AU  - Laizet,S
AU  - Xiao,H
DO  - 10.1016/j.cma.2018.09.010
EP  - 726
PY  - 2019///
SN  - 0045-7825
SP  - 707
TI  - Representation of stress tensor perturbations with application in machine-learning-assisted turbulence modeling
T2  - Computer Methods in Applied Mechanics and Engineering
UR  - http://dx.doi.org/10.1016/j.cma.2018.09.010
UR  - http://hdl.handle.net/10044/1/64109
VL  - 346
ER  -
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