Contact : Herve.Guillard@sophia.inria.fr

Research theme : Numerical algorithms, CFD, plasma physics

Intern level : diplôme d'ingénieur-Engineering school / Mastère-Master's thesis.

Internship duration (months) : from 4 to 6 months

Place of the Internship : Inria Sophia Antipolis and University of Nice, France

Possibility of a follow-up Ph.D or post-doc : Yes

Remuneration : 975 E net

Internship description

This intership is part of a general effort to develop robust and acurate numerical algorithms for the simulation of fusion plasmas in experimental fusion reactors like ITER In the proposed work, we are interested in the modeling and numerical simulation of a two species plasma constituted of electrons and one ion species. A standard description of this plasma consists in a two-fluid model : The Euler equations for each species coupled by a Poisson equation allowing to compute the electric field. In this model, an important dimensionless parameter is the Debye length that measures the typical scale over which charge imbalances can occur. In practical situation, this parameter is usually extremely small compared to the size of the device under study. This leads one to consider quasi-neutral models obtained by formally letting the ratio of the Debye length to the typical size of the device tends to zero. The results being that the two Euler systems are now coupled by an algebraic relation expressing the equality of the charges of the ion and electron fluids instead of being coupled by a Poisson equation. The approximation of these quasi-neutral models are therefore not standard. The aim of this work is to study and compare some numerical strategies to enforce the constraint of quasi neutrality in order to obtain well behaved numerical method.

Prerequisites :

Knowledge in approximation theory of Partial Differential equations, Applied mathematics, CFD or Plasma physics, Good programming skills