No internships offer is available for now.

Previous internships

Subjects of the internships

Since twenty years, fast spectral methods have been developed for simulating rarefied gases. Such physical phenomenon can be modelled with Boltzmann-type equations that are written in 1D+nD+mD in the time-phase space (n = 1,2,3 and m = 2,3).

We are interested in the Boltzmann-Nordheim model where the collision term is trilinear and includes quantum effects of the collisions when the temperature of the gas is low. In such case, Bose-Einstein condensate can occur, which leads to a degenerescence of the distribution function into a combination of a Dirac  delta distribution and a singular Maxwellian distribution.

The aim of this project is the numerical investigation of such phenomenon. Since the Boltzmann-Nordheim model is potentially written in 7D, the numerical methods for discretizing it must be chosen carefully. In 2012, the homogeneous 2D case has been studied by Filbet & al. thanks to fast spectral methods. They also presented some numerical investigations of the approximation of this kinetic model by its macroscopic limit. At present time, we are about to finish the extension to the 3D space homogeneous (n = 0) case. With this new step, we may have the first Bose-Einstein condensate simulations through kinetic modelling.

The aim of the internships is to extend the current work to non-homogeneous cases by discretizing the transport term and extending the numerical methods and codes to 1D+nD+3D with n = 1,2,3 in the phase space. In addition, we aim to speed up the collision computation by improving the existing parallelization techniques.

PRACE Summer of HPC

The internship is funded by the Summer of HPC PRACE 2021 programme and will last 2 months (see SoHPC timeline for the details).

• Starts at : July 4th 2021.

• Ends at ; August 24th, 2021.

The application process is now closed and we are pleased to welcome Artem Mavliutov (Univ. Padovia - Italy) and David Knapp (Univ. Bonn - Germany).

Keywords

Boltzmann equation, kinetic models, discrete Fourier transform, parallel computing.