Caro, Florian (2004) Modélisation and simulation of liquid vapor phase transitions. PhD thesis CMAP, EP - CMAP Centre de Mathématiques Appliquées, EP/X p.226.
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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.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Thesis Supervisor: | Allaire, Grégoire |
| Date: | November 2004 |
| Board of examiners: | Coquel, Frédéric and Despres, Bruno and De vuyst, Florian and Nkonga, Boniface and Saurel, Richard |
| Ecole Doctorale: | ED 447 ECOLE DOCTORALE DE L'ECOLE POLYTECHNIQUE |
| Discipline: | CMAP |
| Collection (Fonds): | EP/X |
| Institution: | EP/X |
| Department: | EP - CMAP Centre de Mathématiques Appliquées |
| Subjects: | 1. Mathematics and Applications |
| Uncontrolled Keywords: | Phase transition, Van Der Waals equation, Visco-capillar criterion, Splitting method, Numerical schemes, Hyperbolicity, Riemann problem, Relaxation, Direct numerical simulation, Transition de phase, équation de Van Der Waals, Critère visco-capillaire, Méthode de splitting, Schéma numérique, Hyperbolicité, problème de Riemann, Relaxation, Simulation numérique directe |
| ID Code: | 993 |
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| Deposited By: | Nadine Garnier |
| Deposited On: | 26 January 2005 |
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