Profile and skills required:
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Applied mathematics, numerical analysis, fluid mechanics, flow instability, aeroacoustics,
noise radiation, Fortran parallel programming
Due to access restrictions, the applicants should be European citizens.

Presentation of the post-doctoral project, context and objective:
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Numerical computation of long-range wave propagation is often expensive since the 
equations are basically elliptic and they must be solved in the whole space domain. 
Therefore, considerable efforts have been devoted for several decades to the 
transformation of the propagation equations into a parabolic system, which can be 
integrated by space marching. In particular, the One Way equations are obtained by 
algebraic factorization of the wave operator. They are used for example to describe the 
propagation of acoustic, seismic or electromagnetic waves. Recently, a modified approach 
combining operator decomposition in the wave direction and numerical discretization in 
the transverse direction has been proposed by Towne & Colonius (2015). One of the key 
advantages of this approach is that it does no longer require tedious algebraic 
factorization and it can therefore be applied to more complex systems of equations, 
such as the linearized Euler or Navier-Stokes equations to describe the propagation 
of waves in inhomogeneous flows.
Two doctoral works have already been carried out at ONERA Toulouse to improve the 
numerical One Way approach and a Fortran code has been developed. The purpose of the 
post-doctoral training will be to continue to improve the code capability and to apply 
it to a practical problem such as the low-frequency sound radiation of jets due to the 
instability of the jet shear layer. First, the growth of fluctuations inside the jet 
shear layer will be computed by One Way method and compared with the results of 
parabolized stability equations (PSE). Then the sound radiation will be deduced and 
compared with LES and experimental data, first for a circular single-stream jet, then 
for a coaxial double-stream jet. The test cases will be defined in coordination with 
Airbus Aircraft and with Pprime Institute, which will also provide experimental data, 
in the frame of a collaborative research program funded by the French Civil Aviation 
Authority.

External collaborations : Airbus Aircraft (Toulouse), Pprime Institute (Poitiers)