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Lagrangian point particle approaches are an attractive solution to model the
presence of a dispersed phase in a carrier phase and are still widely used today
to handle a large variety of applications: combustion, icing, solid propulsion,
etc... One of the main limitations of the Lagrangian approach lies in the
punctual representation of the inclusions and their associated source terms. In
the deterministic context, this makes the standard Lagrangian approach based on
the point-force/ particle-in-cell (PF-PIC) method non convergent with respect to
mesh refinement. Similarly, this poor convergence leads to important
uncertainties on the dispersed phase fields in the stochastic Lagrangian
context. Regularization procedures, where the particle source terms are spread
over a characteristic length scale that is not set by the mesh, may partly
alleviate these convergence issues. The main difference between the
deterministic and stochastic frameworks lies in the fact that for the former,
the regularization length scale is imposed by physical considerations (see Maxey
and Patel, International Journal of Multiphase Flow, 2001) while in the
statistical context, this length scale is mostly dependent on the sampling of
the spray. Strategies to define the regularization length scale and to apply the
regularization procedure in both contexts have been formulated in the PhD thesis
of Poustis performed at ONERA Toulouse, with some open questions in the
stochastic context.

The aim of the current post-doctoral position is therefore twofold. First, the
regularization strategy developed in the stochastic Lagrangian context during
the PhD thesis of Poustis needs to be further investigated and validated.
To save time, these validations may be undertaken in the 2D icing code IGLOO2D
develped at ONERA and used by industrial partners such as Airbus, Dassault
Aviation and Safran Aircraft Engines.

Then, the aim is to transpose these methods to the 3D multiphysics platform
CEDRE developed at ONERA to simulate a large diversity of energetics
applications: combustion, hail and ice ingestion in turbomachines, rocket
propulsion, jet noise, etc... This implies the implementation of a nonlinear
diffusion equation in this platform in order to regularize particle source terms
in the Lagrangian context. Ideally, strategies to further reduce the cost of the
resolution of the nonlinear diffusion equation should be investigated.

References on the subject:

Maxey, M.R. and Patel, B.K., 2001. Localized force representations for particles
sedimenting in Stokes flow. International journal of multiphase flow, Volume 27,
2001, Pages 1603-1626.

Schmidt D.P., Bedford F., An analysis of the convergence of stochastic
Lagrangian/Eulerian spray simulations, International Journal of Multiphase Flow.
Volume 102, 2018, Pages 95-101

Poustis J.F., Senoner J.M., Zuzio D., Villedieu P. Regularization of the Lagrangian
point force approximation for deterministic discrete particle simulations.
International Journal of Multiphase Flow. Volume 117, 2019, Pages 138-152

Poustis J.F., Senoner J.M., Villedieu P. Lagrangian Point Force regularization for
dispersed two-phase flows, Conference paper of the 10th International Conference
on Multiphase Flow, Rio de Janeiro, Brazil, 2019

Practical information:

Position is open immediately until end of 2019
Annual net salary is about 25 000 Euros.
Workplace is ONERA Toulouse, France.

Required skills:

Good knowledge of numerical methods
Good knowledge of the programming language Fortran 90/95 and basic knowledge of
Prior experience in a CFD code used for industrial applications is important
At leat one publications in a peer-reviewed journal is mandatory
Basic French knowledge would be a plus.

If interested, please send a CV with references and a short cover letter to Also, do not hesitate to contact me for futher