Objective of the workshop
In this workshop, we will address the modelling of multiphase flows. The goal is to share modelling methods, difficulties, (rigorous or more phenomenological) analysis, allowing the description of multiphase flows with exchanges (mass transfer, energy exchange…) and apparition of shock waves. Find here the program of the previous workshop.
Several talks are planned, with parts dedicated to open discussions. The main subjects will be a priori:
- the Physics of multiphase flows with mass transfer and high energy exchanges,
- derivation and study of PDE models for compressible multiphase flows,
- construction of coherent thermodynamical laws.
Note that one-velocity and multi-velocity models will be considered.
Program
The talks will start the morning of Monday 30, and finish Tuesday 31 at noon. It will be followed by a workshop on cavitation, bubble collapse and mass transfer (website).
Speakers
Cosmin Burtea
Derivation of a one velocity-one pressure model via homogenization and relaxation
Abstract. In the first part, following the approach developed by M. Hillairet, D. Bresch and X. Huang we recall how to use the theory of Young measures and intermediate weak-solutions à la Hoff in order to obtain one velocity multiphase models with a PDE closure law for the volume fraction. It turns out that the system of PDEs that we obtain can be interpreted as a pressure relaxed Kapila-type model. In the second part of the talk, we present a precise mathematical result concerning the pressure relaxation limit.
Jean Bussac
Généralisation d'un modèle multi-vitesses avec contraintes de miscibilité
Abstract. Ce travail consiste en une généralisation d’un modèle multi-vitesses à N phases immiscibles. Nous y ajoutons une hypothèse de miscibilité sur une des phases, qui peut contenir K composants miscibles. On étudie donc un mélange N-phasique à N+K-1 composants. Les cas N=2, M=3 et N=3, M=4 ont été étudiés récemment. L’analyse du modèle (hyperbolicité, symétrisation) est présentée, et nous démontrons que sous des conditions classiques, les termes interfaciaux en pression existent et sont définis d’une unique manière. Des classes de termes sources admissibles sont également étudiées.
Gloria Faccanoni
Thermal Diffusion with Phase Transition in a Heat Exchanger
Abstract. This work is devoted to the modelling a liquid-vapour flows with phase transition describing the evolution of the coolant within an heat exchanger (e.g. the core of a Pressurized Water Reactor). We investigate a low Mach number model enriched with a degenerate thermal diffusion. We focus on the influence of the thermal diffusion on a simple configuration for which some analytical computations can be done.
Sergey Gavrilyuk
How to determine the Leidenfrost temperature?
Arthur Loison
Two-scale dyamic polydisperse reduced order model for two-phase flows
Charlotte Perrin
Well-posedness of partially congested Navier-Stokes equations
Abstract. This talk addresses the mathematical analysis of 1D Navier-Stokes equations including a maximum packing constraint, that is a maximal constraint on the density. These equations arise naturally in the modeling of mixtures like suspensions or in the modeling of collective motion. The main feature of the model is the co-existence of two different phases. In the congested phase, the pressure is free and the dynamics is incompressible, whereas in the non-congested phase, the fluid obeys a pressureless compressible dynamics. I will discuss the Cauchy problem for initial data which are small perturbations in the non-congested zone of travelling wave profiles. This is a joint work with Anne-Laure Dalibard.
Philippe Villedieu
Modèles à interface diffuse pour la modélisation des phénomènes de mouillage partiel : du microscopique au macroscopique
Abstract. Dans cet exposé je montrerai comment on peut utiliser une approche macroscopique de type "champ de phase" et le principe de moindre action pour obtenir une famille de modèles qui permettent de décrire les phénomènes de mouillage à différentes échelles. On peut les nommer "modèles à ligne triple diffuse" car ils possèdent des analogies avec les "modèles à interface diffuse" utilisés les écoulements diphasiques. En particulier, l’expression de la force capillaire au niveau de la ligne triple ne fait pas intervenir une mesure de Dirac ou une pression de disjonction mais le gradient d'une fonction "couleur" (le champ de phase) que l'on peut interpréter comme un paramètre d'ordre variant continument de 0 à 1 à travers une zone d'épaisseur finie modélisant la ligne triple.
Contributions
A poster session will be organized Monday. If you are interested in presenting your recent works in the topics of the workshop, we would be happy to welcome you. Please contact the organizers, sending a title and an abstract of your poster. For those who would like to submit their contribution without being present, online 15 minute-long talks will be possible too.
Practical informations
Location
Institut de Recherche Mathématique Avancée, Strasbourg (map).
Restaurant
Rendez-vous lundi soir à 20h au restaurant La Victoire : 24 quai des Pêcheurs, Strasbourg.
Organizing committee
Philippe Helluy, Jean-Marc Hérard, Nicolas Seguin.
