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Modélisation et simulation numérique des transitions de phase liquide vapeur.

Abstract : This work deals with the modelization and numerical simulation of liquid-vapor phase transition phenomena. The study is divided into two part: first we investigate phase transition phenomena with a Van Der Waals equation of state (non monotonic equation of state), then we adopt an alternative approach with two equations of state. In the first part, we study the classical viscous criteria for selecting weak solutions of the system used when the equation of state is non monotonic. Those criteria do not select physical solutions and therefore we focus a more recent criterion: the visco-vapillar criterion. We use this criterion to exactly solve the Riemann problem (which imposes solving an algebraic scalar non linear equation). Unfortunately, this step is quite costly in term of CPU which prevent from using this method as a ground for building Godunov solvers. That is why we propose an alternativ approach two equations of state. Using the least action principle, we propose a phase changing two-phase flow model which is based on the second thermodynamic principle. We shall then describe two equilibrium submodels issued from the relaxations processes when instantaneous equilibrium is assumed. Despite the weak hyperbolicity of the last submodel, we propose stable numerical schemes based on a two-step strategy involving a convective step followed by a relaxation step. We show the ability of the system to simulate vapor bubbles nucleation.
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https://pastel.archives-ouvertes.fr/pastel-00000993
Contributor : Ecole Polytechnique <>
Submitted on : Tuesday, July 27, 2010 - 9:46:36 AM
Last modification on : Wednesday, March 27, 2019 - 4:08:30 PM
Long-term archiving on: : Thursday, October 28, 2010 - 11:23:01 AM

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Florian Caro. Modélisation et simulation numérique des transitions de phase liquide vapeur.. Mathématiques [math]. Ecole Polytechnique X, 2004. Français. ⟨pastel-00000993⟩

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