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Modélisation d’écoulements compressibles avec transition de phase et prise en compte des états métastables

Abstract : The main objective of this work is the modelling of liquid-vapor phase change and the understanding of the apparition of metastable states which appear in the van der Waals equation of state (EOS). A metastable state corresponds to a gaseous (or liquid) state which, after a slight perturbation, changes into the liquid (or gaseous) state quickly. In the first part, we first study all the properties of the van der waals EOS in its isothermal and non-isothermal representations. Then, we study the optimization problem under constraints, which allows us to characterize the thermodynamic equilibrium and the maximum number of phases that may be present at the thermodynamic equilibrium. We construct three dynamical systems in the isothermal case, which minimize the Helmoltz free energy and whose equilibria coincide with the thermodynamical equilibrium . They are the stable and metastable liquid and vapor states and the coexistence state. Finally, this technique is extended to the non-isothermal case where we construct two dynamical systems satisfying the same properties. In the second part, we are interested in the coupling of thermodynamics with the fluid dynamics. We first study the Riemann problem for the isothermal p-system with a van der Waals EOS coupled to the Maxwell correction. Then, we stuy the travelling waves of a relaxed p-system in order to understand the discontinuities of its equilibrium system. Finally, dynamical systems constructed in the first part are coupled to isothermal and non-isothermal two-phase hyperbolic systems. Numerical results are presented throughout this manuscript to illustrate the theoretical results we obtained.
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Submitted on : Wednesday, January 9, 2019 - 6:52:48 PM
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Hala Ghazi. Modélisation d’écoulements compressibles avec transition de phase et prise en compte des états métastables. Equations aux dérivées partielles [math.AP]. Université de nantes, 2018. Français. ⟨tel-01976189⟩

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