Second Workshop on Compressible Multiphase Flows

May 27, 2019, 1:00 PM → May 29, 2019, 3:00 PM Europe/Paris

IRMA, université de Strasbourg

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.

A dozen of talks is planned, with several 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 afternoon of Monday 27, and finish Wednesday 29 at noon. Open discussions will also be possible during the morning of Monday 27 and the afternoon of Wednesday 29.

Speakers

Each talk will last 40 minutes and be followed by a session of 20 minutes for open discussions.

• Didier Bresch
• Pierre Cordesse
• Steinar Evje
• Sergey Gavrilyuk
• Vincent Giovangigli
• Samuel Kokh
• Hélène Mathis
• Charlotte Perrin
• Romain Privat
• Christian Rohde
• Khaled Saleh
• Philippe Villedieu

Poster session

The poster will be held Tuesday at 5:30pm, with the following contributions:

• Hamza Boukili
• Clément Cancès
• Jean-marc Hérard
• Lucie Quibel

Practical informations

Location
Institut de Recherche Mathématique Avancée, Strasbourg (map).

Lunch
Restaurant for Tuesday lunch: location
32 Boulevard de la Victoire, 67000 Strasbourg
Warning: you have to go to the highest floor. 

Dinner
Restaurant "La Victoire" at 19h30: location
24 Quai des Pêcheurs, 67000 Strasbourg

Organizing committee

Philippe Helluy, Jean-Marc Hérard, Nicolas Seguin.

 

 

Boukili.pdf

Herard.pdf

Quibel.pdf

Monday, May 27

1 Equations of state: capabilities and limitations

Speaker: Romain Privat (Université de Lorraine)

3:00 PM Coffee break

2 Two-fluid model hierarchy - thermodynamics, non-conservative terms and hyperbolicity/entropic symmetrization

Speaker: Pierre Cordesse (École Oolytechnique)

3 Uncertainty principle in two--fluid mechanics

Hamilton’s principle (or the principle of stationary action) is one of the basic modelling tools in classical mechanics. It states that the reversible motion of a mechanical system is completely determined by the corresponding Lagrangian which is the difference between the kinetic and potential energy of the system.
The extension of Hamilton’s principle to the continuum mechanics involving fluid-fluid and solid-fluid interaction can be performed (cf. [1, 2]). The motion of a multi–fluid continuum is described by a coupled system of “Newton’s laws” for each component that are completely determined by the Lagrangian. The introduction of dissipative terms compatible with the second law of thermodynamics and natural mathematical restrictions on the potential energy allow us to derive the governing equations having nice mathematical properties.
I will present here a simplest example of two-velocity flows where one of the phases is incompressible (for example, flows of dusty air, or flows of compressible bubbles in an incompressible fluid). A very surprising fact is that one can obtain different governing equations from the same Lagrangian. Different types of the governing equations are due to the choice of independent variables and the corresponding virtual motions. The equations differ from each other in the presence (or not) of gyroscopic forces (also called “lift” forces). The total energy does not depend on these forces, but the velocity distribution depends on them. The gyroscopic forces are not usually taken into account in two-fluid models. Even if these forces have no influence on the hyperbolicity of the governing equations, their presence drastically changes the distribution of the energy of each component.
To the best of my knowledge, such an uncertainty in the governing equations of multi-phase flows was never a subject of discussion in a “multi-fluid” community.
[1] S. Gavrilyuk, Multiphase flow modelling via Hamilton’s principle, In the book : F. dell’Isola, S. L. Gavrilyuk (Editors), Variational Models And Methods In Solid And Fluid Mechanics, Springer, 2011.
[2] S. Ndanou, N. Favrie, S. Gavrilyuk, Multi-solid and multi-fluid diffuse interface model: applications to dynamic fracture and fragmentation, J. Comput. Phys. 295(2015) 523–555.

Speaker: Sergey Gavrilyuk (Aix-Marseille Université)

Tuesday, May 28

4 A Saint-Venant type model to simulate the dynamics of thin partially wetting films

Speaker: Philippe Villedieu (Onera)

10:00 AM Coffee break

5 A multiphase model to understand how aggressive tumor cell behavior is linked to elevated fluid flow

Speaker: Steinar Evje (University of Stavanger)

6 TBA

Speaker: Charlotte Perrin (CNRS & Aix-Marseille université)

12:30 PM Lunch

7 A three-phase flow model with two miscible phases

Speaker: Hélène Mathis (Université de Nantes)

3:00 PM Coffe break

8 Derivation and analysis of a model for N-phase non miscible compressible flows

Speaker: Khaled Saleh (Université de Lyon 1)

9 Transcritical Hydrogen/Oxygen flames

Speaker: Vincent Giovangigli (École Polytechnique)

10 Poster session

Boukili.pdf

Herard.pdf

Quibel.pdf

Wednesday, May 29

11 On Brenner's Two Velocity Hydrodynamics

In a series of papers over 9 years (2004-2012), Howard Brenner (1929--2013) [who was emeritus professor at MIT in chemical engineering] proposed a new theory in compressible fluid mechanics with high gradient of density based on the concept of two different velocities: the mass and the volume velocities. At the same time, D.B. with B. Desjardins discovered (with E. Zatorska later on) that a structure with two velocity hydrodynamics already exists in standard models (i.e. with one velocity field) if the shear and the bulk viscosities satisfy the BD algebraic relation. In this talk, I will try to to give an historical overview of this mathematical story and explain at the end a recent mathematical result with A. Vasseur and C. Yu.

Speaker: Didier Bresch (CNRS & Université Savoie Mont Blanc)

10:00 AM Coffee break

12 A Multiscale Sharp Interface Approach for Resolved Liquid-Vapour Flow

Speaker: Christian Rhode (University of Stuttgart)

13 TBA

Speaker: Samuel Kokh (CEA Saclay)