Croissance et coalescence de bulles dans les magmas : analyse mathématique et simulation numérique

Abstract : This thesis is devoted to mathematical and numerical study of a physical problem coming from volcanology. We look at the polydisperse modeling of bubbles growth by exsolution, decompression and coalescence. A polydisperse growth model has been proposed in literature, but it takes into accountonly the volume of bubbles, which restrict the application field, because growth by exsolution also depends on the water mass in the bubbles. In order to upgrade this model, we start with a non-dimensional monodisperse description of the bubble growth by decompression and exsolution, given by a coupled ODE system and a PDE. A numerical code is proposed to solve the monodisperse problem and is currently used. After validating this code numerically and considering several limit cases, we studied the solutions of the system and defined a flux approximation to decouple the equations system. Next, we extend the polydispers model from one to two dimensions, the volume and the water mass of bubbles. A resolution of coalescence is proposed and coupled with the polydisperse growth model. The resolution of coalescence is confronted with others numericals schemes in one and two dimensions in order to validate the proposed numerical scheme. The first numerical tests applied to a physical problem give good results.
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Louis Forestier-Coste. Croissance et coalescence de bulles dans les magmas : analyse mathématique et simulation numérique. Mathématiques générales [math.GM]. Université d'Orléans, 2012. Français. ⟨NNT : 2012ORLE2012⟩. ⟨tel-00736634⟩

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