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From neutrino radiative transfer in core-collapse supernovae to fuzzy domain based coupling methods

Defense Thèse de doctorat : Univ. Genève, 2015 - Sc. 4767 - 2015/02/16
Abstract This thesis consists in two parts: In the first part, we study the approximation of neutrino radiative transfer in core-collapse supernovae. In particular, we study the Isotropic Diffusion Source Approximation (IDSA). To do so, we first rederive the asymptotic limits used in this approximation using Hilbert and Chapman-Enskog expansions. We then show, using a model problem, that the coupling mechanism used in the IDSA can lead to unphysical solutions. We finally propose some corrections for the homogeneous sphere test case. In the second part, we introduce the framework of Fuzzy Domain Decomposition Methods (FDDMs). These methods are heterogeneous domain decomposition methods characterized by a time-dependent volumic adaptive coupling. We compare these methods with classical domain decomposition methods and quantify the approximation error for a simple class of 1D model using Matched Asymptotic Expansions (MAE). Finally, we formulate a time-dependent FDDM.
Keywords Supernovae modelingBoltzmann equationRadiative transferHilbert expansionChapman-Enskog expansionHomogeneous sphereDomain decomposition methodsFuzzy setsFuzzy domain decomposition methodsMatched asymptotic expansions
URN: urn:nbn:ch:unige-549397
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Research group Analyse numérique
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MICHAUD, Jérôme. From neutrino radiative transfer in core-collapse supernovae to fuzzy domain based coupling methods. Université de Genève. Thèse, 2015. doi: 10.13097/archive-ouverte/unige:54939 https://archive-ouverte.unige.ch/unige:54939

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Deposited on : 2015-03-30

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