A three-year PhD position is available in the CFD & Aeroacoustics Department at
ONERA starting from October 2013.

Location: ONERA - Châtillon (south of Paris)

Title: Wavelet-based multiscale simulation of turbulent flows 

In the framework of the Aghora project, Onera is currently working on the
development of high-order methods for the simulation of turbulent flows using
DNS and LES. Within this line of research, we propose here to investigate an
alternative high-order method which exploits the remarkable properties of the
wavelet-based multiresolution analysis (MRA) technique .

In recent work, we have developed a multilevel approach to LES which relies on
the wavelet-based MRA technique to separate the flow into its large and
small-scale components. To this end, the N-S equations are projected onto a
hierarchy of scaling function (coarse grid) and wavelet spaces (fine grids) at
different levels of resolution. The proposed approach has been assessed by using
a priori testing on data from DNS. A posteriori (dynamic) tests have been only
performed for decaying and force-driven (1D) Burgers turbulence.

In this thesis, we propose to extend this methodology to the simulation of 3D
incompressible turbulent flows using second generation wavelets (SGW). In a 3D
transform domain, the formulation of the LES problem becomes more involved, as
the number of wavelet subspaces per resolution increases sevenfold with respect
to 1D. It may be possible, however, to reduce the number of degrees of freedom
of the problem by neglecting the contribution of certain wavelet spaces.
Research along this line will be carried out by analysing available DNS data. An
effective coding strategy for the implementation of the incompressible solver
based on SGW will be designed. The final implementation should also incorporate
a spatially adaptive wavelet thresholding strategy able to exploit the
sparseness property of the wavelet representation. An interesting challenge in
the formulation of the incompressible problem is the treatment of the mass
conservation and pressure subgrid-scale terms, which arise from the projection
operation. The PhD student will carefully investigate this point in order to
select the most appropriate approach to deal with these terms. A suitable
modelling strategy will also be developed in order to account for the unresolved
scales (discarded wavelet spaces). Finally, LES computations on a number of
reference test cases will be performed and compared against DNS data.  

Entry requirements: Candidates will have a degree in Engineering, Physics or
Applied Mathematics, and a strong background in CFD, numerical methods and fluid
dynamics, ideally acquired through postgraduate research. 

If interested, please send a detailed CV, cover letter and grade transcripts to
Dr Marta de la Llave (email: marta.de_la_llave_plata@onera.fr). You should also
consider sending two recommendation letters to support your application. 

Closing date for applications: open until a suitable candidate is found.

Further details can be found at

http://sites.onera.fr/formationparlarecherche/sites/sites.onera.fr.formationparlarecherche/files/DSNA-2013-02.pdf