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AbstractAbstract
[en] In this thesis, I described my work at CEA-DAM. During these 15 years, I have proposed numerical methods to solve different models in the framework of radiative compressible hydrodynamics. The problems addressed in this manuscript are extensive and deal with the resolution of parabolic and hyperbolic systems. The common points of this work are the observation of fundamental principles, which have guided it: consistency with the system of equations to be solved, respect of conservation laws, and stability (in the sense non-linear stability and respect of the mathematical or physical constraints of the systems of equations). Once these specifications were met, I focused on ensuring other important properties of the systems of equations under consideration, such as Galilean invariance, respect of equilibrium or asymptotic limits. The continuation of this work is already under way and is based on two axes: the enhancement of the order of approximation and the extension of the model. (author)
[fr]
Dans cette these, j'ai decrit mon travail au CEA-DAM. Durant ces 15 annees, j'ai propose des methodes numeriques pour resoudre differents modeles dans le cadre de l'hydrodynamique radiative compressible. Les problemes abordes dans ce manuscrit sont vastes et portent sur la resolution de systemes paraboliques et hyperboliques. Les points communs de ce travail sont l'observation de principes fondamentaux qui l'ont guide: coherence avec le systeme d'equations a resoudre, respect des lois de conservation, et stabilite (au sens stabilite non lineaire et respect des contraintes mathematiques ou physiques des systemes d'equations). Une fois ces specifications remplies, je me suis attache a garantir d'autres proprietes importantes des systemes d'equations consideres, comme l'invariance galileenne, le respect de l'equilibre ou des limites asymptotiques. La suite de ce travail est deja en cours et s'articule autour de deux axes: l'amelioration de l'ordre d'approximation et l'extension du modeleOriginal Title
Contribution a la simulation numerique de l'hydrodynamique radiative
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17 Dec 2021; 67 p; 185 refs.; Available from the INIS Liaison Officer for France, see the INIS website for current contact and E-mail addresses; Mathematiques; These habilitation a diriger les recherches
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