Contribution à la résolution des équations de la magnétohydrodynamique et de la magnétostatique.

Abstract : Interaction between a plasma and a magnetic field appears and has an important role in various domains such as thermonuclear fusion by magnetic confinement or astrophysical plasmas for example. In evolution, these interactions are described by the equations of magnetohydrodynamics (MHD). At equilibrium, the MHD equations reduce to the magnetostatic equations involving the magnetic field and the kinetic pressure of the plasma.
The magnetostatic equations form a system of 3D non linear partial differential equations involving a magnetic field and a kinetic plasma pressure. When the pressure is supposed negligible, the magnetic field is known as Beltrami field. In a first time, we propose to solve numerically the Beltrami fields problem using a fixed point iterative algorithm associated with finite element methods. This iterative strategy is extended in a second time to the computation of magnetostatic configurations with pressure.
In the sequel, we interest in the approximation of ideal MHD equations. This system forms a nonlinear hyperbolic conservation law. We propose to use a finite volume approach, in which fluxes are calculated by a Roe's method on a tetrahedral mesh. Fluxes of the magnetic field are modified in order to satisfy the constraint of divergence free imposed on it.
The proposed methods have been implemented in two new three dimensional codes called TETRAFFF for equilibrium, and TETRAMHD for MHD. The obtained numerical results confirm the high performance of these methods.
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Submitted on : Monday, December 17, 2007 - 6:12:31 PM
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Cédric Boulbe. Contribution à la résolution des équations de la magnétohydrodynamique et de la magnétostatique.. Mathématiques [math]. Université de Pau et des Pays de l'Adour, 2007. Français. ⟨tel-00196421v2⟩

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