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Job Record #15511
TitleAugmentation of measurements through data assimilation
CategoryPhD Studentship
LocationFrance, Meudon
InternationalYes, international applications are welcome
Closure DateSaturday, June 01, 2019
Title: Augmentation of experimental measurements based on stochastic data
assimilation approaches

Several efficient experimental techniques, and in particular Particle Image
Velocimetry (PIV) [1],  are now available to obtain unsteady velocity fields in
a whole domain of interest in complex and turbulent flow configurations.
However, these techniques may still be limited in terms of spatial and temporal
resolutions and dimensions of the investigated domain. In particular, it remains
difficult nowadays to obtain accurate velocity measurements over large
three-dimensional domains or close to solid walls.

An emerging approach to increase the resolution of experimental data consists in
combining them with computational fluid dynamics (CFD) tools, so that the
measurements are extrapolated, and their resolution and smoothness improved,
while being constrained by the numerically resolved conservation laws of fluid
motion. This so-called data assimilation (DA) [2] approach has been implemented
in two different ways so far. The first one consists in minimizing the
discrepancies between the experimental data and the predictions of a CFD solver
relying on optimal control theory [3,4]. While indeed providing enhanced
estimations of the measured flow fields, a drawback of this technique is the
need of the development of the adjoint model associated to the considered CFD
solver, which may be a tedious task and implies heavy computational burden. The
second approach is based on the stochastic (Bayesian) formulation of the DA
problem, where the statistics related to the confidence in a numerical
prediction are sequentially updated in time using the available data. Depending
on the degree of approximation of the shape of these statistics, one can derive
various DA schemes, from particle filters [5] that solve the full DA problem,
taking into account all sources of nonlinearity, to more operational Kalman
filters [6,7]. These techniques do not require the coding of an adjoint model,
and can thus be readily implemented. However, they may be still limited by the
relatively large computational cost required to propagate in time the statistics
associated to the flow state, which is usually equivalent to 10-100 forward
simulations and may be the main bottleneck in the application of such DA
approaches to complex flow configurations.

The present PhD plan aims at developing operational stochastic DA techniques
that can be used to augment the resolution and extrapolate time-dependent
experimental data (obtained from PIV or PTV) for various flow configurations.
These techniques should be versatile (easily used in conjunction with different
CFD solvers) and require limited computational cost (around a few forward
simulations). State-of-the-art Kalman filter-based techniques will be first
considered and adapted to the studied flows. In particular, the physics (e.g.
incompressibility [8]) and the statistical properties of the flow (e.g.
statistically steadiness [9]) will be exploited in order to decrease as much as
possible the computational cost of the DA procedure. Further adjustments to take
into account model errors, for example to correct a turbulence model [7], or
strong nonlinearities [10] could also be considered.

The PhD will take place in the framework of an internal research project at
ONERA, in which several demonstrations of DA are foreseen. More specifically,
the methodological developments undertaken will be motivated by an experimental
campaign planned during the second year of the PhD. Before this campaign, the
candidate will be able to validate and test the newly developed approaches on
already existing numerical or experimental data (such as jet, flow over backward
facing step, or around a wall-mounted cube). As for the newly performed
demonstration experiments, the configuration will be that of an obstacle (bluff
body or wing profile in incidence, to be determined) in a water channel at
Reynolds numbers of the order of 5,000 to 10,000, and measured by several
techniques, including 3D high-speed PIV/PTV, unsteady force and friction
sensors, among others. The PhD candidate will process the experimental data
(depending on his/her interests, direct participation to the experimental
campaign is also possible), and then apply the developed DA algorithms. In this
process, the objective will be to assess the extent of augmentation achieved,
such as space/time super-resolution, denoising, interpolation and extrapolation.
Also, interesting questions to tackle within this evaluation will be the
robustness of the techniques to sparse data, i.e. to quantify the minimum
experimental input necessary for them to work in practice. Such questions are
among the crucial ones in research on these techniques, the underlying interest
being the conception of future experiments in terms of types and numbers of

[1] Raffel, Willert, Wereley and Kompenhans, Particle Image Velocimetry: A
practical Guide, Springer, 2007.
[2] Lewis, Lakshmivarahan and Dall, Dynamic Data Assimilation approach: A Least
Squares Approach, Cambridge University Press, 2006.
[3] Gronskis, Heitz and Mémin, Inflow and initial conditions for direct
numerical simulation based on adjoint data assimilation, J. Comput. Phys., 2013.
[4] Yegavian, Leclaire, Champagnat and Marquet, Performance assessment of PIV
super-resolution with adjoint-based data assimilation, 11th Int, symp, on
particle image velocimetry, Santa Barbara, USA, 2015.
[5] Combés, Heitz, Guibert and Mémin, A particle filter to reconstruct a
free-surface flow from a depth camera, Fluid Dyn. Res., 2015.
[6] Suzuki, Reduced-order Kalman-filtered hybrid simulation combining particle
tracking velocimetry and direct numerical simulation, J. Fluid Mech., 2012.
[7] Kato, Yoshizawa, Ueno and Obayashi, A data assimilation methodology for
reconstructing turbulent flows around aircraft, J. Comput. Phys., 2015.
[8] Meldi, Poux, A reduced order model based on Kalman filtering for sequential
data assimilation of turbulent flows, J. Comput. Phys., 2017.
[9] Sumihar, Verlaan and Heemink, Two-Sample Kalman Filter for Steady-State Data
Assimilation, Mon. Wea. Rev., 2008.
[10] Van Leeuwen, Cheng, Reich, Nonlinear data assimilation, Springer, 2015.

Period: September 2019-September 2022

Profile of the candidate: Master 2/Engineer school in Fluid Mechanics
Contact Information:
Please mention the CFD Jobs Database, record #15511 when responding to this ad.
NameVincent Mons
Email ApplicationYes
8 rue des Vertugadins
92190, Meudon, France
Record Data:
Last Modified14:49:27, Thursday, December 06, 2018

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