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Couplage interfacial de modèles en dynamique des fluides. Application aux écoulements diphasiques.

Thomas Galié 1
1 LETR - Laboratoire d'Etudes Thermiques des Réacteurs
DM2S - Département de Modélisation des Systèmes et Structures : DEN/DM2S/SFME/LETR
Abstract : This thesis is devoted to the study of interface model coupling problems in space between different models of compressible flows. We consider one-dimensional problems where the interface is sharp, fixed and separating two regions of space corresponding to the two coupled models. Our goal is to define a coupling condition at the interface and to solve numerically the coupling problem with this condition. After a state of art on the interface model coupling of hyperbolic systems of conservation laws, we propose a new coupling condition by adding in the equations of the coupled problem a measure source term at the interface. We first suppose a given constant weight associated to this source term. Two Riemann solvers are developped and one of them is based on a relaxation approach preserving equilibrium solutions of the coupled problem. This relaxation method is then used in an optimization problem, defined by several motivations at the interface, which permits to calculate a time dynamical weight. In a second part, we develop an approached Riemann solver for a two-phase two-pressure model in the particular case of a two-phase isentropic flow. Such a model contains non conservative terms that we write under the form of measure source terms.
The previous relaxation method is thus extended to the case of the two-phase two-pressure model with an a priori estimation of the non conservative term contributions. The method allows us to solve, in the next and last chapter, the coupling problem of a two-fluid two-pressure model with a drift-flux model thanks to the father model approach.
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Submitted on : Monday, June 15, 2009 - 11:03:13 PM
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Thomas Galié. Couplage interfacial de modèles en dynamique des fluides. Application aux écoulements diphasiques.. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2009. Français. ⟨tel-00395593⟩

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