Skills required:
Applied mathematics, numerical analysis, fluid mechanics, flow instability,
aeroacoustics, Fortran parallel programming

Nationality:
Due to access restrictions, this position is only open for European Union citizens.

Job description:
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 (Poitiers, France), which will also 
provide experimental data, in the frame of a collaborative research program funded by 
the French Civil Aviation Authority.