# Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows

Europe/Paris
Amphi Hermite (Institut Henri Poincaré)

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
Description

Flows with liquid-vapor transfer occur at many different scales in the atmosphere as well as in many industrial processes. It would be interesting to have a general review of the topic before focusing on the simpler geometry involving a single liquid-vapor interface. An objective of the workshop will be to discuss the relative merits and to compare different numerical methods (if the single liquid-vapor interface is still too complex, the comparison could be made on a liquid-gas interface without mass transfer). It could be also interesting to find clear-cut problems in order to make quantitative comparisons between different models or with experimental results.

The registration is free of charge but mandatory. Lunch and coffee break will be offered.

Where : Institut Henri Poincaré, Paris, France (map here).

When : december 12-13, 2016.

Program (pdf) : see here.

Registration : see here.

A 3D bubble with Adaptative Mesh Refinement

(A. Talpaert - CEA Paris-Saclay)

Invited speakers :

• Marie Béchereau (Ecole normale supérieure de Cachan, Paris-Saclay)
• Guillaume Bois (CEA Paris-Saclay)
• Hélène Mathis (Université de Nantes)
• Richard Saurel (Université d'Aix-Marseille)
• Arthur Talpaert (CEA et Ecole Polytechnique, Paris-Saclay)
• Laurette Tuckerman (Ecole Supérieure de Physique et de Chimie Industrielle de Paris)
• Stéphane Zaleski (Université Pierre et Marie Curie, Paris)

3D bubbles with averaging plane

(G. Bois - CEA Paris-Saclay)

Participants
• Anne Burbeau
• Anouar MEKKAS
• Antoine du Cluzeau
• Arthur Talpaert
• Benjamin Graille
• Benoit-Joseph Grea
• Bertrand Mercier
• Bérénice Grec
• Caterina Calgaro
• Cedrick Copol
• Chaouki HABCHI
• Christophe Chalons
• Christophe Josserand
• Colette Nicoli
• Daniel Fuster
• Daouda SANGARE
• Dena Kazerani
• Elie Hachem
• Emmanuel Creusé
• Florian De Vuyst
• François Dubois
• François-Xavier Demoulin
• Garon André
• Giovanni Ghigliotti
• Grégoire Allaire
• Guillaume BOIS
• Guillaume Sahut
• Gérard Gallice
• Gérard Liger-Belair
• HASSAN BARKAI ALLATCHI
• Hélène Mathis
• Ibrahima CISSE
• Jean-Marc CARRAT
• Julien CARLIER
• Julien Derr
• Karol Cascavita
• Laurent Martin Witkowski
• Laurette Tuckerman
• Lucien Vienne
• Marc Massot
• Marc Medale
• Marco De Lorenzo
• Maria Giovanna Rodio
• Marica Pelanti
• Marie Bechereau
• Marié Simon
• Mehdi Khalloufi
• Michel Delfour
• Nicolas Grenier
• Nicolas Maquignon
• Olivier Heuzé
• Philippe Cordier
• Philippe Lafon
• Picella Francesco
• Pierre HALDENWANG
• Pietro Marco Congedo
• Rafael Lugo
• Raviart Pierre-Arnaud
• Renaud Motte
• Renée Gatignol
• Richard Saurel
• Rudy Valette
• Rémi Abgrall
• Saira Pineda
• Shanggui Cai
• Simon PELUCHON
• Songzhi Yang
• Stephan Fauve
• Stéphane Dellacherie
• Stéphane Zaleski
• Sébastien Tanguy
• Thibaut Ménard
• Thomas Leroy
• Vincent Giovangigli
• Vitoriano Ruas
• Wen YANG
• Yannick Hoarau
• Yohan Penel
Support
• Monday, 12 December
• 08:30 09:00
WELCOME 30m Hall d'accueil, Institut Henri Poincaré

### Hall d'accueil, Institut Henri Poincaré

• 09:00 09:45
Effervescence in champagne and sparkling wines: Recent advances and future prospects 45m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
Bubbles in a glass of champagne may seem like the acme of frivolity to most of people, but in fact they may rather be considered as a fantastic playground for any fluid physicist. In a glass of champagne, about a million bubbles will nucleate and rise if you resist drinking from your flute. The so-called effervescence process, which enlivens champagne and sparkling wines tasting, is the result of the complex interplay between carbon dioxide (CO2) dissolved in the liquid phase, tiny air pockets trapped within microscopic particles during the pouring process, and some both glass and liquid properties. The journey of yeast-fermented CO2 is reviewed (from its progressive dissolution in the liquid phase during the fermentation process, to its progressive release in the headspace above glasses). The physicochemical processes behind the nucleation, and rise of gaseous CO2 bubbles, under standard tasting conditions, have been gathered hereafter. Moreover, when a bubble reaches the air-champagne interface, it ruptures, projecting a multitude of tiny droplets in the air. Based on the model experiment of a single bubble bursting in simple liquids, we depict each step of this process, from bubble bursting to droplet evaporation. In particular, we demonstrate how damping action of viscosity produces faster and smaller droplets and more generally how liquid properties enable to control the bubble bursting aerosol characteristics. We demonstrate that compared to a still wine, champagne fizz drastically enhances the transfer of liquid into the atmosphere. Conditions on bubble radius and wine viscosity that optimize aerosol evaporation are provided. These results pave the way towards the fine tuning of aerosol characteristics and flavor release during sparkling wine tasting, a major issue of the sparkling wine industry.
Speaker: Prof. Gérard Liger-Belair (CNRS)
• 09:45 10:30
Direct Numerical Simulation of Bubbles with Adaptive Mesh Refinement with Distributed Algorithms 45m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
This talk presents the implementation of the simulation of two-phase flows in conditions of water-cooled nuclear reactors, at the scale of individual bubbles. To achieve that, we study several models for Thermal-Hydraulic flows and we focus on a technique for the capture of the thin interface between liquid and vapour phases. We thus review some possible techniques for Adaptive Mesh Refinement (AMR) and provide algorithmic and computational tools adapted to patch-based AMR, which aim is to locally improve the precision in regions of interest. More precisely, we introduce a patch-covering algorithm designed with balanced parallel computing in mind. This approach lets us finely capture changes located at the interface, as we show for advection test cases as well as for models with hyperbolic-elliptic coupling. The computations we present also include the simulation of the incompressible Navier-Stokes system, which models the shape changes of the interface between two non-miscible fluids. We highlight two canonical test cases: the (one-phase) lid-driven cavity as well as the Rayleigh-Taylor instability.
Speaker: Mr Arthur Talpaert (CEA and Ecole Polytechnique (Paris-Saclay))
• 10:30 11:00
PAUSE 30m Hall d'accueil, Institut Henri Poincaré

### Hall d'accueil, Institut Henri Poincaré

• 11:00 11:30
Numerical simulations of gas/vapor bubble oscillations 30m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
In this work we numerically investigate the effect of heat and mass transfer on the dynamic response of gas-vapor bubbles. The numerical solution of the full non-linear 1D equations is compared with the analytical solution of the equations obtained for the oscillation of an spherical gas/vapor bubble in response of a weak pressure perturbation (linear solution). For a system with known gas/vapor/liquid properties, we identify various oscillation regimes as a function of an nondimensional oscillation frequency (e.g. the bubble's Peclet number) and the vapor content. Even at very low frequencies, there exist regimes where transient diffusion effects arise due to heat diffusion in the surrounding liquid and also due to vapor mass diffusion inside the bubble. These phenomena restrict the applicability of the commonly-adopted assumption of full-equilibrium conditions inside the bubble. Simulations of the oscillation of bubbles for strong perturbations shows that non-linear effects restrict even further the range of applicability of the isothermal equilibrium model when the vapor content becomes larger than a critical value.
Speaker: Dr Daniel FUSTER (Institut D'Alembert, UPMC-CNRS 75005 Paris)
• 11:30 12:00
Simulation of free surface fluids in incompressible dynamique 30m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
In this work, we present a numerical scheme for solving free surface flows. The free surface is modeled using the level-set formulation. Besides, the mesh is anisotropic and adapted at each iteration. This adaptation allows us to obtain a precise approximation for the free- surface location. In addition, it enables us to solve the time-discretized fluid equation only on the fluid domain. The fluid here is considered incompressible. Therefore, its motion is described by the incompressible Navier–Stokes equation which is temporally discretized using the method of characteristics and is solved at each time iteration by a first order Lagrange–Galerkin method. The level-set function representing the free surface satisfies an advection equation which is also solved using the method of characteristics. The algorithm is completed by some intermediate steps like the construction of a convenient initial level-set function (redistancing) as well as the construction of a convenient flow for the level-set advection equation. Finally, some numerical results are presented.
Speaker: Mrs Dena Kazerani (Laboratoire Jacques-Louis Lions (UPMC, Paris 6))
• 12:00 12:30
Direct Numerical Simulation of Liquid-Vapor Phase Change. Applications to Leidenfrost Droplet and Nucleate Boiling 30m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
Studies on two-phase flows are of interest in many fundamental problems and industrial applications, as the spray formation in internal combustion engine, the bubble formation in heat exchangers, the fluid management in satellites or space launcher tanks, the spray cooling or the interaction of bubbles with acoustic waves. The Direct Numerical Simulation is a powerful tool, which is complementary to experimental measurements, to provide accurate results in complex situations. However, unlike single-phase flows, currently the direct numerical simulation of two- phase flows cannot be considered as a fully mature field, especially in most configurations involving strong coupling between the interface motion with heat and mass transfer, acoustic or shock waves, and/or a solid boundary where a contact line can be formed. This presentation will emphasize on the development of new numerical methods [1,2,3,4,5] to perform accurate Direct Numerical Simulations of two-phase flows with phase change in the framework of sharp interface capturing numerical methods. The presentation will focus mainly on two specific configurations involving liquid vapor phase change, i.e. Leidenfrost droplets and nucleate boiling. We will discuss about suited numerical strategy to succeed numerical simulations in these configurations. Accurate comparison between experiments and fully-resolved numerical simulations will be presented in order to bring out the relevance of the proposed algorithms. [1] S. Tanguy, T. Menard, A. Berlemont, A level set method for vaporizing two-phase flows, J. Comput. Phys. 221 (2007) 837-853 [2] S. Tanguy, M. Sagan, B. Lalanne, F. Couderc, C. Colin, Benchmarks and numerical methods for the simulation of boiling flows. J. Comput. Phys. 264 (2014) 1-22. [3] L. Rueda Villegas, R. Alis, M. Lepilliez, S. Tanguy. A Level Set/Ghost Fluid Method for boiling flows and liquid evaporation: Application to the Leidenfrost effect. J. Comp. Phys. 316 (2016) 789-813 [4] L. Rueda Villegas, S. Tanguy, G. Castanet, O. Caballina, F. Lemoine. Direct Numerical Simulation of the impact of a droplet onto a hot surface above the Leidenfrost temperature. Int. J. Heat Mass Transfer 104 (2017) 1090-1109 [5] G. Huber, M. Sagan, C. Colin, S. Tanguy. Direct Numerical Simulation of nucleate boiling at moderate Jakob number and high microscopic contact angle. In preparation to be submitted in Int. J. Heat Mass Transfer
Speaker: Dr Sébastien Tanguy (Institut de Mécanique des Fluides de Toulouse)
• 12:30 14:15
LUNCH TIME 1h 45m Hall d'accueil, Institut Henri Poincaré

### Hall d'accueil, Institut Henri Poincaré

• 14:15 15:00
Numerical simulation of flows with sharp interfaces by the Volume-Of-Fluid method 45m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
We discuss recent developments in the Volume-Of-Fluid (VOF) methods, such as the height function method for the approximation of the geometry of the interface, the balanced-force surface tension method, and the methods that conserve mass and momentum at machine accuracy. Applications at high Reynolds number,such as high speed liquid-gas flows, and low Reynolds and low Capillary numbers, are discussed. Problems of engineering and physical interest, such as jet atomisation or flow in porous media are investigated with these methods as will be shown.
Speaker: Prof. Stéphane Zaleski (Université Pierre et Marie Curie (Paris))
• 15:00 15:45
Applications of the Front-Tracking algorithm of TrioCFD to turbulent bubbly flows in plane channels 45m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
The Front-Tracking method has been implemented in TrioCFD and improved over the last decade. It has been widely used on large parallel architectures to study incompressible two- phase flows. The permanent increase in computing capabilities allows to perform simulations of fully turbulent bubbly flows in relatively small periodic domains. This talk will be organized in two parts. The numerical method used to perform Front-Tracking simulations will be presented. The code is capable to deal with phase change and specific Ghost-Fluid Methods have been implemented to guarantee a great accuracy of the solution, even in the presence of large jumps and phase change. Then, recent calculations on adiabatic two-phase turbulent bubbly flows will be presented. Averaged results are analyzed in great details in order to better understand the dominant processes in the exchange mechanisms at the interface and in the modulation of turbulence by the vapor inclusions and their wakes. Preliminary results and suggestions for the two-fluid model will conclude the presentation. This work was granted access to the HPC resources of TGCC under the allocation 20XX- t20142b7239 made by GENCI.
Speaker: Dr Guillaume Bois (CEA (Paris-Saclay))
• 15:45 16:30
PAUSE 45m Hall d'accueil, Institut Henri Poincaré

### Hall d'accueil, Institut Henri Poincaré

• 16:30 17:00
High fidelity anisotropic adaptive FEM towards physical couplings occurring in turbulent boiling 30m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
We propose in this work an adaptive variational multiscale method for complex multiphase flows with surface tension: applications to 3D bubble dynamics, turbulent boiling and solid quenching with experimental comparisons will be presented. A new conservative level-set method is used to provide a precise position of the interfaces. An implicit implementation of the surface tension in the context of the Continuum Surface Force is proposed to circumvent the capillary time step restriction. The obtained system is then solved using a unified compressible-incompressible variational multiscale stabilized finite element method designed to handle the abrupt changes at the interface and large density and viscosity ratios. Combined with an a posteriori error estimator, we show that anisotropic mesh adaptation yields an accurate 3D modeling framework for turbulent multiphase flows with phase change.
Speaker: Dr Elie Hachem
• 17:00 17:30
Modelling atomization with phase change 30m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
DNS[1], LES [2] and RANS [3] modelling of atomization have been developed for the last decade in our laboratory with a particular attention devoted on the behavior of the interface. In particular model equations for the liquid-gas surface density have been proposed based on the pioneering work of Borghi and Vallet [4]. The purpose of this approach is to determine the surface density that we believe is the first order parameter to determine the mass transfer rate, a key future of fuel injection system. In addition to well-developed procedures usually used to evaluate the vaporization rate for dispersed spray based on the resolution of Boltzmann-Williams kinetic equation, our focus has been to determine the phase change rate for any kind of interface geometry not only spherical droplet. To do so the interface capturing DNS code Archer has been extended to handle heat and mass transfer at the interface based on the method proposed by Tanguy et al. [5], [6]. From this work the turbulent mixing of a scalar quantity issued from an interface such has the vapor concentration has been studied showing the importance of interface boundary layer zone on the global statistic of the scalar field [7]. Further works concern the extension of interface capturing method generally based on incompressible scheme to fully compressible code to handle other phenomena occurring during the injection process such as cavitation. [1] T. Menard, S. Tanguy, et A. Berlemont, « Coupling level set/VOF/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet », Int. J. Multiph. Flow, vol. 33, n o 5, p. 510‐524, 2007. [2] J. Chesnel, J. Reveillon, T. Menard, et F. X. Demoulin, « Large eddy simulation of liquid jet atomization », At. Sprays, vol. 21, n o 9, p. 711‐736, 2011. [3] R. Lebas, T. Menard, P. A. Beau, A. Berlemont, et F. X. Demoulin, « Numerical simulation of primary break-up and atomization: DNS and modelling study », Int. J. Multiph. Flow, vol. 35, n o 3, p. 247‐260, 2009. [4] A. Vallet et R. Borghi, « Modélisation Eulerienne de L’atomisation d’un Jet Liquide », C R Acad Sci Paris Sér II B, vol. 327, p. 1015–1020, 1999. [5] S. Tanguy, T. Ménard, et A. Berlemont, « A Level Set Method for vaporizing two-phase flows », J. Comput. Phys., vol. 221, n o 2, p. 837‐853, 2007. [6] B. Duret, T. Menard, J. Reveillon, et F. X. Demoulin, « Two phase flows DNS of evaporating liquid-gas interface including interface regression, using Level Set and Coupled Level Set/VOF method », présenté à 8th International Conference on Multiphase Flow (ICMF 2013, 2013. [7] B. Duret, G. Luret, J. Reveillon, T. Menard, A. Berlemont, et F. X. Demoulin, « DNS analysis of turbulent mixing in two-phase flows », Int. J. Multiph. Flow, vol. 40, n o 0, p. 93‐105, 2012.
Speaker: Dr François-Xavier Demoulin (CORIA)
• 17:30 18:00
Locally conservative approximation of (conservative) systems written in non conservation form: application to Lagrangian hydrodynamics and multifluid problems 30m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
Since the celebrated Lax Wendroff theorem, it is known that the right way of discretising systems of hyperbolic equations written in conservation form is to use a flux formulation. However, in many occasions, the relevant formu- lation, from an engineering point of view, is not to consider this conservative formulation but one non conservative form. For example, with standard notations, a one fluid model writes [équation : voir résumé PDF] (1) but the interesting quantities are the mass, velocity and pressure, which evolution is described by: [équation : voir résumé PDF] (2) Unfortunately this form is not suitable to approximation. In the case of a multi-fluid system, the same problem occurs. In this talk, we will describe a method to overcome this issue. It does not use any flux formulation per se, but can be shown to provide the right solutions. In order to illustrate the method, we will consider several examples in Eulerian and Lagrangian hydrodynamics We will first start from the Residual Distribution (RD) (re-)interpretation of the Dobrev et al. scheme [1] for the numerical solution of the Euler equations in Lagrangian form. The first ingredient of the original scheme is the staggered grid formulation which uses continuous node-based finite element approximations for the kinematic variables and cell-centered discontinuous finite elements for the thermodynamic parameters. The second ingredient of the Dobrev et al. scheme is an artificial viscosity technique applied in order to make possible the computation of strong discontinuities. Using a reformulation in term of RD scheme, we can show that the scheme is indeed locally conservative while the formulation is stricto sensu non conservative. Using this, we can generalise the construction and develop locally conservative artificial viscosity free schemes. To demonstrate the robustness of the proposed RD scheme, we solve several one-dimensional shock tube problems from rather mild to very strong ones: we go from the classical Sod problem, to TNT explosions (with JWL EOS) via the Collela-Woodward blast wave problem. In a second part, we show how to extend this method to the Eulerian framework and give applications on single fluid and multiphase problems via the five equation model. References [1] V. Dobrev, T. Kolev, and R. Rieben. High order curvilinear finite element methods for Lagrangian hydrodynamics. SIAM J. Sci. Comput, 34:B606–B641, 2012.
Speaker: Prof. Rémi Abgrall (Université de Zürich)
• 18:00 18:30
END OF DAY 1 30m
• Tuesday, 13 December
• 09:00 09:45
Modelling liquid-vapor phase change with metastable states 45m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
We propose a model of liquid-vapor phase transition including metastable states of the van der Waals Equation of State. The first part of the talk concerns the thermodynamics model. Following the second principle, the problem boils down to a minimization problem with constraints of the mixture energy. This ”static” description allows to recover the classical equilibria: pure liquid/vapor states and a coexistence state (given by the Maxwell equal area rule). Then, when assuming a dependency with respect to time, we define a dynamical sys- tem with long time equilibria which are either the classical equilibria or the metastable states. In a second part of the talk, we use the dynamical system as a source term of a two-phase isothermal model. The homogeneous model is hyperbolic under condition. However for smooth solutions, we manage to prove that the regions of hyperbolically are invariant domains. We finish with some numerical experiments, obtained by a finite volume scheme and a splitting technique to handle the source term.
Speaker: Dr Hélène Mathis (Université de Nantes)
• 09:45 10:30
Diffuse interfaces with compressible fluids, phase transition and capillarity 45m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
Conventional models of capillary fluids with phase transition consider linked thermodynamics and capillarity. Such coupling has serious consequences, such as: - sound propagation, undefined in some critical regions, - very thin interfaces, causing serious issues in practical computations. In the present talk an approached based on hyperbolic systems with relaxation is promoted to solve interfaces with phase transition and surface tension. The method deals with arbitrary pressure and density jumps. The diffuse interface model consists in a set of balance equations of mass for each phase and momentum and energy for the mixture. When simple contact is considered (in the absence of heat diffusion), a volume fraction equation is needed as well. In this frame each phase is compressible and governed by its own (convex) equation of state, preserving sound propagation. The two equations of state are rendered compatible through appropriate constants determined from the phase diagram. Phase change is modeled through Gibbs free energy relaxation terms. Capillarity is modelled through mass fraction gradients at interfaces and is consequently decoupled of thermodynamics. Examples of cavitating, flashing and boiling flows with and without shocks are shown. Le Métayer, O., & Saurel, R. (2016). The Noble-Abel Stiffened-Gas equation of state. Physics of Fluids 28(4), 046102 Saurel, R., Le Metayer, O. and Boivin, P. (2016) A general formulation for cavitating, boiling and evaporating flows. Computers and Fluids 128, 53-64 Le Martelot, S., Saurel, R. and Nkonga, B. (2014) Toward the direct numerical simulation of boiling flows. Int. J. of Multiphase Flows 77, 62-78 Le Martelot, S., Nkonga,B. and Saurel, R. (2013) Liquid and liquid–gas flows at all speeds, Journal of Computational Physics 255(15), 53-82 Petitpas, F., Massoni, J., Saurel, R., Lapebie, E. and Munier, L. (2009) Diffuse interface model for high speed cavitating underwater systems. Int. J. Multiphase Flow 35, 747-759 Saurel, R., Petitpas, F. and Abgrall, R. (2008) Modeling phase transition in metastable liquids. Application to flashing and cavitating flows. Journal of Fluid Mechanics, 607:313-350
Speaker: Prof. Richard Saurel (Université Aix-Marseille)
• 10:30 11:00
PAUSE 30m Hall d'accueil, Institut Henri Poincaré

### Hall d'accueil, Institut Henri Poincaré

• 11:00 11:45
Numerical simulation of Faraday wave patterns 45m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
In 1831, Faraday described the standing wave patterns that form on the surface of a layer of fluid subjected to periodic vertical vibration. These waves usually take the form of stripes, squares, or hexagons. However, other phenomena have been observed numerically, such as quasipatterns, supersquares, heteroclinic cycles, and oscillons. Until recently, numerical simulation of Faraday waves was out of reach. Since 2009, however, we have simulated not only simple wave patterns but also patterns which involve large-scale modulation. To do so, we have developed a massively parallel multiphase code, BLUE, whose treatment of the free surface uses a hybrid Front-Tracking/Level-Set technique, defining the interface both by a discontinuous density field on the Eulerian grid and by triangles on the Lagrangian interface mesh. We will discuss the various Faraday wave configurations we have studied: regular square and hexagonal lattices, patterns composed of spherical harmonics on a vibrated drop, and supersquares consisting of a four-by-four array of smaller squares.
Speaker: Prof. Laurette Tuckerman (Ecole Supérieure de Physique et de Chimie Industrielle (Paris))
• 11:45 12:30
Lagrange-Euler Lattice-Boltzmann Method And Its Application to Two-Fluid Flows Dynamics With Possibly High Density Ratio 45m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
Two-fluid extensions of Lattice Boltzmann methods with free boundaries usually consider "microscopic'' pseudopotential interface models. In this paper, we rather propose an interface-capturing Lattice Boltzmann approach where the mass fraction variable is considered as an unknown and is advected. Several works have reported the difficulties of LBM methods to deal with such two-fluid systems especially for high-density ratio configurations. This is due to the mixing nature of LBM, as with Flux vector splitting approaches for Finite Volume methods. We here give another explanation of the lack of numerical diffusion of Lattice Boltzmann approaches to accurately capture contact discontinuities. To fix the problem, we propose an arbitrary Lagrangian-Eulerian (ALE) formulation of Lattice-Boltzmann methods. In the Lagrangian limit, it allows for a proper separated treatment of pressure waves and advection phenomenon. After the ALE solution, a remapping (advection) procedure is necessary to project the variables onto the Eulerian Lattice-Boltzmann grid. We explain how to derive this remapping procedure in order to get second-order accuracy and achieve sharp stable oscillation-free interfaces. It has been shown that mass fractions variables satisfy a local discrete maximum principle and thus stay in the range $[0,1]$. The theory is supported by numerical computations of the free fall of an initial square block of a dense fluid surrounded by a lighter fluid into a box. Figures 1 and 2 are showing the mass fraction field of the light fluid at two successive instants. The density ratio equal to 4 and the computational lattice grid is 400x400. One can appreciate the thickness of the numerical diffuse interface, the capture of complex structures and the capability to compute strong changes of free boundary topology. Even if our methods are currently used for inviscid flows (Euler equations) by projecting the discrete distributions onto equilibrium ones at each time step, we believe that it is possible to extend the framework formulation for multifluid viscous problems. This will be at the aim of a next work.
Speaker: Mrs Marie Béchereau (Ecole normale supérieure de Cachan (Paris-Saclay))
• 12:30 14:30
LUNCH TIME 2h Hall d'accueil, Institut Henri Poincaré

### Hall d'accueil, Institut Henri Poincaré

• 14:30 15:00
Benchmarking rotating flow with free surface deformation 30m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
The free surface deformation generated by a disk rotating at the bottom of a container partially filled with fluid is an exciting challenge for numerical simulations. The shape of the free surface has shown surprising patterns in experiments performed by different research groups. However, for many regimes (non axisymmetric, dewetted disk, sloshing), an accurate comparison with numerical simulations is clearly missing. We will present the different existing regimes of such flow and show results of comparison between different numerical codes on few selected regimes. Some preliminary measurements on a recent experimental set up will also be presented and we will discuss the relevance of a benchmark on such flow.
Speaker: Dr Laurent Martin Witkowski
• 15:00 15:30
Numerical simulation of a gas bubble collapse using the SPH-ALE method 30m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
A multiphase model developed in SPH-ALE is used to simulate the collapse of a gas bubble in water. This model does not diffuse the interface and guarantees the continuity of normal velocity and pressure at the interface between both fluids. This scheme is able to deal with interfaces of simple contact where normal velocity is continuous. The model solves the mass, momentum and energy conservation equations of Euler system using a non-isentropic equation of state for each phase, the Stiffened Gas EOS for water and the ideal gas EOS for the gas bubble. Both phases are compressible and the phase change is not modeled. A multiphase shock tube is presented for validation purpose, with satisfactory results in comparison with reference solutions. The dynamics of the Rayleigh collapse of a bubble in a free-field and near a planar rigid wall are analyzed. Collapse behavior, interfacial velocities and surface pressure as a function of time are analyzed for the free-field collapse case, and in addition, as a function of the initial bubble stand-off distance from the wall for the case of the bubble collapse near the wall. For the case of the bubble collapse near a wall, a re-entrant jet directed towards the surface is observed due to the non- symmetry initial configuration. The potential damage to the surface wall is estimated by measuring the wall pressure.
Speaker: Mrs Saira Pineda
• 15:30 16:00
Simulations of a heated fluid at low Mach number: modelling of phase transition and numerical strategies 30m Amphi Hermite

### Amphi Hermite

#### Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris, France
Thermohydraulic codes used in industry are based on the resolution of compressible Navier-Stokes equations in which acoustic waves are taken into account. This allows to describe fluid flows at any Mach number. However, many difficulties may arise in terms of CPU time, robustness and accuracy in the low Mach number regime. In this regime, an asymptotic expansion with respect to the Mach number leads to simpler models. Thus, the strategy of our work is to derive, investigate and simulate a system of PDE taking into account phase transition in the low Mach number regime but with possible high heat transfers. More precisely, we focus on the choice of the equation of state and its parameters, with emphasis on the gain due to the low Mach number hypothesis, and we present preliminary 2D numerical simulations with FreeFem++ showing the robustness of the approach. This is a joint work with S. Dellacherie, G. Faccanoni and Y. Penel.
Speaker: Dr Bérénice Grec
• 16:00 16:30
PAUSE 30m Hall d'accueil, Institut Henri Poincaré

### Hall d'accueil, Institut Henri Poincaré

• 16:30 17:00
END OF DAY 2 30m