Mathematical and numerical analysis of the resistive magnetohydrodynamics system with self-generated magnetic field terms

Abstract : This work is devoted to the construction of numerical methods that allow the accurate simulation of inertial confinement fusion (ICF) implosion processes by taking self-generated magnetic field terms into account. In the sequel, we first derive a two-temperature resistive magnetohydrodynamics model and describe the considered closure relations. The resulting system of equations is then split in several subsystems according to the nature of the underlying mathematical operator. Adequate numerical methods are then proposed for each of these subsystems. Particular attention is paid to the development of finite volume schemes for the hyperbolic operator which actually is the hydrodynamics or ideal magnetohydrodynamics system depending on whether magnetic fields are considered or not. More precisely, a new class of high-order accurate dimensionally split schemes for structured meshes is proposed using the Lagrange-remap formalism. One of these schemes' most innovative features is that they have been designed in order to take advantage of modern massively parallel computer architectures. This property can for example be illustrated by the dimensionally split approach or the use of artificial viscosity techniques and is practically highlighted by sequential performance and parallel efficiency figures. Hyperbolic schemes are then combined with finite volume methods for dealing with the thermal and resistive conduction operators and taking magnetic field generation into account. In order to study the characteristics and effects of self-generated magnetic field terms, simulation results are finally proposed with the complete two-temperature resistive magnetohydrodynamics model on a test problem that represents the state of an ICF capsule at the beginning of the deceleration phase.
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Mathematics [math]. Université de Strasbourg, 2011. English. 〈NNT : 2011STRA6101〉
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  • HAL Id : tel-00632428, version 1



Marc Wolff. Mathematical and numerical analysis of the resistive magnetohydrodynamics system with self-generated magnetic field terms. Mathematics [math]. Université de Strasbourg, 2011. English. 〈NNT : 2011STRA6101〉. 〈tel-00632428〉



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