École Nationale Supérieure de
Techniques Avancées

Abstract

This internship takes place in the context of the inertial confinement fusion experiments carried out at the Laser MegaJoule by the CEA. In order to design and interpret 3D experiments, with an imposed external magnetic field, the simulation codes must evolve. We are interested in the resistive contributions of the Braginskii model, which closes the magnetohydrodynamic equations. These terms make it possible to establish a prototype equation, by constituting an electric field of resistive origin, operating in the magnetic field induction equation. First, a mathematical analysis of this equation is performed in order to identify an adequate discretization strategy. An implicit finite volume scheme for the magnetic field is then proposed and studied on unstructered meshes. It is based on a divergence-preserving discretization of the rotational operators. Finally, several numerical experiments are conducted to demonstrate the relevance of the scheme.