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Job Record #15394
TitlePostdoc: Machine Learning-augmented Turbulence Modelling
CategoryPostDoc Position
LocationFrance, MEUDON
InternationalYes, international applications are welcome
Closure DateFriday, March 01, 2019
It is well-known that current RANS turbulence models suffer from inaccuracies in
some complex configuration (separations, corner flows, laminar/turbulent
transition). Despite the continuous increase in computing power, direct and
large eddy simulations at realistic Reynolds numbers (107) will remain too
expensive for several decades. This is the reason why RANS simulations will
remain the main tool in CFD for aircraft design for the next years. Industrial
use of CFD requires thousands of computations for design optimisation on the
full aircraft flight envelope beyond the limits of which RANS models are known
to be inaccurate. Moreover, industrial expectations on CFD accuracy have risen
(maximum lift error below 5%, parasitic drag error below 2%…). Hybrid RANS/LES
simulations are gaining more and more attention but they are still too expensive
for routine use and require a high level of user skill. In addition, they still
rely on a turbulence model close to the wall so they can suffer from the same
issues than RANS simulations. The most used turbulence models in CFD today (SA,
k-ω) have been designed thirty years ago and they have been calibrated on a
limited number of academic test cases hence the inaccuracies in complex
configurations. Since several years, one can observe a stagnation in RANS model
improvements possibly because of a lack of new ideas, or possibly because of a
glass ceiling. More recent, Reynolds Stress Transport (RST) models are nonlinear
in nature and closer to turbulence physics. Consequently, they improve accuracy
but they also rely on some constants which are harder to calibrate because of a
higher degree of model complexity. Moreover, they do not predict flows
systematically better than widely-used one- or two equation models.
Recent progresses in machine or deep learning open new ways to assimilate large
databases (>106). The availability of large amounts of high-resolution data from
both experiments (PIV) and DNS/LES leads to the idea of combining machine
learning tools with CFD to create machine learning-augmented turbulence models
[1-4]. The objective of the present post-doctoral position is to develop such
data-driven turbulence models. Rather than throwing away the existing knowledge
in turbulence modeling, one idea is rather to build on top of it by improving
existing turbulence models by adding corrective terms. 
The flow chart below presents the different steps of the post-doctoral project.
The first step is a “field inversion” or data assimilation one since the data
(corrective term on the production in SA model for example here) that we want to
find is not measurable. This is done by minimising the L2-norm of the error on
the velocity between a reference field (higher fidelity simulation like ZDES
here) and a RANS-SA computation. This requires an adjoint solver to find the
gradient of the objective function in each grid cell. Once these data generated
on several test cases to explore all situations where turbulence models suffer
from inaccuracies, a neural network is trained to estimate these data from
computable quantities (velocity gradients for example). Then, a new RANS
simulation can be performed using a neural network corrected turbulence model.

• Study of different strategies on the assimilated variable (eddy viscosity,
Reynolds stresses, corrective term in classical turbulence models, …)
• Selection of test cases exploring configurations where actual linear eddy
viscosity turbulence models (SA, k-ω) suffer from inaccuracies (separation,
corner flow, …) and for which experimental or DNS/LES data are available
• Data inference or field inversion phase step on each test case: creation of a
large database of assimilated variable 
• Study of neural network structures dedicated to turbulence modelling
• Deep learning on GPU

[1] Singh, A.P., Medida, S., Duraisamy, K., Machine Learning-augmented
Predictive Modeling of Turbulent Separated Flows over Airfoils, AIAA Journal,
55(7):2215-2227, 2017.
[2] Parish, E., Duraisamy, K., A paradigm for data-driven predictive modeling
using field inversion and machine learning, Journal of Computational Physics,
305:758–774, 2016.
[3] Ling, J., Jones, R., Templeton, J., Machine learning strategies for systems
with invariance properties, Journal of Computational Physics, 318:22–35, 2016.
[4] Franceshini, L., Fabbiane, N., Marquet, O., Dandois, J., Leclaire, B., Sipp,
D., Data-driven turbulence modeling applied to separated flows, UMich/NASA
Symposium on Advances in Turbulence Modeling, Ann Arbor, 11-13 July 2017.

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Email ApplicationYes
Address8, rue des Vertugadins
Record Data:
Last Modified14:40:14, Monday, October 15, 2018

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