11th DFG–CNRS WORKSHOP Micro-Macro Modeling and Simulation of Liquid-Vapor Flows

organized with the financial support of


Wednesday March 2nd, 2016 (afternoon) 

to  Friday March 4th, 2016 (at noon)

Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4, Place Jussieu, Paris. Subway station: Jussieu 

Lecture room 15-16 — 309



Nina Aguillon (Paris) 

Christophe Berthon (Nantes)

Christophe Chalons (Versailles) 

Frédéric Coquel (Palaiseau)

Johannes Daube (Freiburg)

Bruno Després (Paris)

Christian Dickopp (Aachen)

Florence Drui (Châtenay-Malabry) 

Robert Eymard  (Marne-La-Vallée)

Jan Giesselman (Stuttgart)

Philippe Helluy (Strasbourg)

Mirko Kraenkel (Freiburg)

Dietmar Kroener (Freiburg)

Rüdiger Müller (Berlin)

Carlos Pares (Malaga)

Arnold Reusken (Aachen)



Main organizer

Philippe G. LeFloch (Paris)


Dietmar Kroener (Freiburg)

Frédéric Coquel (Palaiseau)



Wednesday afternoon (Chairman P.G. LeFloch) 


14h30 -15h Robert Eymard  (Marne-La-Vallée)
15h – 15h30 Jan Giesselman (Stuttgart)
15h30 – 16h Coffee break
16h-16h30 Philippe Helluy (Strasbourg)
16h30-17h Mirko Kraenkel (Freiburg)


Thursday morning  (Chairman Jan Giesselman)


10h-10h30 Christophe Berthon (Nantes)
10h30-11h Johannes Daube (Freiburg)
11h-11h30 Coffee break 
11h30-12h Christophe Chalons (Versailles)
12h-12h30 Dietmar Kroener (Freiburg)
12h30-14h30 Lunch break


Thursday afternoon (Chairman F. Coquel) 


14h30-15h Bruno Després (Paris)
15h-15h30 Arnold Reusken (Aachen)
15h30-16h Coffee break
16h-16h30 Nina Aguillon (Paris)
16h30-17h Rüdiger Müller (Berlin)


Friday morning (Chairman D. Kroener)


10h-10h30 Carlos Pares (Malaga)
10h30-11h Florence Drui (Châtenay-Malabry)
11h-11h30 Coffee break
11h30-12h Christian Dickopp (Aachen)
12h-12h30 Frédéric Coquel (Palaiseau)




Nina Aguillon (Paris)  Numerical approximation of hyperbolic systems containing an interface 
Abstract. We present an approach to approximate numerically the solution of coupled hyperbolic conservation laws. The coupling is achieved through a fixed interface, in which interface conditions are linking the traces on both sides. The main interest of the scheme is that it does not use the knowledge of the solution to the Riemann problem, and hence it is quite flexible and easy to implement. The idea of the scheme is to balance the effects ot the waves that enter the interface, in order to numerically mimic the structure of the Riemann problem. The scheme is well balanced with respect to all the piecewise equilibria associated with the interface conditions. If one of the interface condition is the conservation of a conserved variable, the scheme maintains it exactly. We will present a detailed analysis in the classical case, and a variety of test cases assessing the quality of the method. This is a joint work with Raul Borsche (Technische Universität Kaiserslautern)

Christophe Berthon (Nantes)  Numerical convergence rate for a diffusive limit of hyperbolic systems: p-system with damping


Christophe Chalons (Versailles)  On all regime Lagrangian-remap numerical schemes for compressible fluid systems
Abstract. It is the purpose of this contribution to provide an overview on recent advances in the development of all-regime Lagrange-Remap numerical schemes for compressible fluids systems with source terms. We will consider in particular the case of large friction coefficients and the case of low-Mach numbers. More precisely, we will present a discretization strategy for gas dynamics equations for unstructured grids based on a Lagrange-Remap approach that does not involve any moving mesh. A natural semi-implicit extension of the method that allows to remain stable under a CFL condition involving only the material velocity will be given, together with an extremely simple modification that allows to provide an accurate and stable solver for simulations involving low-Mach regions in the flow. The stability properties of the proposed schemes and several numerical experiments will be presented. This contribution is based on a series of joint works with Mathieu Girardin and Samuel Kokh. These works were performed during M. Girardin’s PhD thesis.


Johannes Daube (Freiburg)  Sharp interface limit for the Navier–Stokes–Korteweg model

Abstract. The Navier–Stokes–Korteweg model, an extension of the compressible Navier–Stokes equations, is a diffuse interface model for liquid-vapour flows which allows for phase transitions. In the model, a small parameter represents the thickness of an interfacial area, where phase transitions occur. Its static version was studied by Hermsdoerfer, Kraus and Kroener and the corresponding interface conditions were obtained. Assuming convergence of an associated energy functional to a suitable surface measure, we will perform the sharp interface limit in the dynamic case. More precisely, by means of compactness, we will ensure that solutions to the diffusive Navier-Stokes-Korteweg equations converge to solutions of an appropriate sharp interface model as the interface thickness tends to zero. This is joint work with H. Abels (Regensburg), C. Kraus (Wuerzburg-Schweinfurt) and D. Kroener (Freiburg).


Bruno Després (Paris) Modeling uncertainties with  kinetic equations
Abstract: The modeling of uncertainties is fundamental in industry and in CFD. For  nonlinear equations, it   questions the compatibility of L1-BV techniques (for conservation laws)  with L2 approaches (for the uncertainties). I will review recent progresses on the modeling at the kinetic level (with B. Perthame), and present recent ideas  which show connection of the so-called kinetic polynomials with optimal control (with E. Treat).


Christian Dickopp (Aachen) Coupling of (elastic)-plastic solids with compressible two-phase fllows for cavitation damaging
Abstract. As a model problem to investigate cavitation damaging the collapse of a single gas bubble collapsing near to an elastic or elastic-plastic solid wall is simulated numerically. This transient three-phase system is  modeled by the compressible Euler equations completed by a stiffened gas law for both fluids, where the liquid and the gas phase are distinguished  by a level set approach, and either the pure elastodynamical equations for a linear-elastic solid or an extension to describe plastic effects. A weak coupling strategy connects the alternating calculations of the fluid solver and  the solid solver using transient boundary conditions that are updated by the other solver.


Florence Drui (Châtenay-Malabry) A hierachy of homogeneous two-fluid models and numerical methods for simulating various regimes of two-phase flows
Abstract. Compressible two-fluid models offer a potential solution for simulating separated two-phase flows configurations. On the other hand, a specific family of such models has been developed for the regime of dispersed gas bubbles and show good agreement with experiments in the case of small acoustic perturbations. On the way to connect both types of flows, we propose here a hierarchy of homogeneous two-fluid models. Starting with Hamilton’s variational principle and adding thermodynamically consistent dissipative structures, we built a new connected hierarchy, each level of which being mathematically well-posed. Every new relaxation small parameter is physically identified through acoustic linearization and analysis of the systems dispersion relations. Furthermore, numerical methods based on finite volume schemes are developed so as to preserve the properties of the models at the continuous level and to asymptotically handle the transition from each subsystem to another. Finally, simulations of simple academic configurations are performed and show the expected properties of the first models of the hierarchy, the numerical methods and dynamically adaptive mesh techniques with the potential for massively parallel simulations.


Robert Eymard  (Marne-La-Vallée) Convection and total variation flow
Abstract. We consider a simplified model, related to the flow of a nonNewtonian fluid. This simplified model consists in a scalar nonlinear hyperbolic equation, regularized by the total variation flow operator (or 1-Laplace operator). We give an entropy weak formulation, for which we prove the uniqueness of the solution using the doubling variable technique. We provide an existence result using the convergence of a numerical scheme, a splitting scheme where the hyperbolic flow is treated with finite volumes and the total variation flow with finite elements. Finally, some numerical simulations in 1D and 2D are presented. This work is a joint work with F. Bouchut and D. Doyen.


Jan Giesselman (Stuttgart) A priori error analysis of DG approximations of two-phase flows

Abstract. In this talk we consider a one dimensional  model for isothermal two-phase flows using Lagrangian coordinates. The model is of diffuse interface type with a non-monotone pressure law. We will present a priori error analysis of a semi-discrete discontinuous Galerkin method, which satisfies a discrete version of the energy inequality which is valid on the continuous level. It also satisfies a relative energy type stability theory. Combining this stability framework with suitable projection operators for the exact solution allows us to derive optimal order error estimates. We will also present numerical results obtained using a fully-discrete version of the scheme, which validate our theoretical results.


Philippe Helluy (Strasbourg) Task-based parallelization of a transport discontinuous Galerkin solver and applications.
Abstract. We present an implicit discontinuous Galerkin solver for the transport equation. Due to the upwind nature of the numerical flux, the linear system in the implicit step is block triangular. The scheme is thus well adapted to a task-based implementation. We present such an implementation using the StarPU library and we  discuss applications to fluid dynamics.


Mirko Kraenkel (Freiburg) Discontinuous Galerkin schemes for the Navier-Stokes-Allen-Cahn system


Dietmar Kroener (Freiburg) Conservation laws on surfaces


Rüdiger Müller (Berlin)  The Lippmann equation for liquid metal electrodes
Abstract. The Lippmann equation is considered as universal relationship between interfacial tension, double layer charge, and cell potential. Recently we have derived a general thermodynamically consistent model for electrochemical interfaces, which shows a remarkable agreement to single crystal experimental data. In this talk, we apply the model to a curved liquid metal electrode in contact with an electrolyte. By matched asymptotic analysis we obtain the Lippmann equation whenever the Debye length is small compared to electrode curvature radius. The interfacial tension of the Lippmann equation is composed of the surface tension of our general model, and additional contributions arising from the adjacent space charge layers. Comparison with experimental data of several mercury-electrolyte interfaces confirms the theoretical results. This is a joint work with Wolfgang Dreyer, Clemens Guhlke, and Manuel Landstorfer.


Carlos Pares (Malaga) Nonconservative products and Shallow Water models: an overview
Abstract. Many hyperbolic nonlinear PDE systems that include source terms and nonconservative products arise in the simulation of geophysical flows by means of depth-averaged models.  In this talk, a review of the numerical techniques developed in last years by my group of research and collaborators to solve this type of systems will be presented together with a discussion of the main difficulties  and challenges in this field. Some applications to the simulation of real flows will be shown to illustrate this topic.


Arnold Reusken (Aachen) Space-time unfitted FEM for problems with moving discontinuities
Abstract. In this talk we will discuss unfitted finite element methods (or CutFEM) in  a space-time setting. The motivation for the development of these methods comes from two-phase incompressible flows. We explain how these techniques can be applied for the accurate discretization of a mass transport equation and a two-phase flow (Navier-)Stokes equation. The idea of the method, rigorous error bounds for certain problem classes and results of numerical experiments will be presented.

Partial LIST of Participants
Boris Andreianov       boris.andreianov at lmpt.univ-tours.fr
Robert Eymard            robert.eymard at univ-mlv.fr
Jan Giesselmann      jan.giesselmann@mathematik.uni-stuttgart.de
Philippe Helluy      helluy at math.u-strasbg.fr
Mirko Keaenkel                kraenkel at mathematik.uni-freiburg.de
Bruno Despres          despres at ann.jussieu.fr
Christophe Berthon   christophe.berthon at math.univ-nantes.fr
Philippe LeFloch      contact at philippelefloch.org
Ruediger Mueller       mueller at wias-berlin.de
Arnold Reusken            reusken at igpm.rwth-aachen.de
Carlos Parés       pares at anamat.cie.uma.es
Johannes Daube              hannes at mathematik.uni-freiburg.de
Chalons Christophe christophe.chalons@uvsq.fr
Nina Aguillon      aguillon at ljll.math.upmc.fr
Christian Dickopp      dickopp at web.de
Florence Drui           florence.drui at centralesupelec.fr
Emmanuel Audusse     eaudusse at yahoo.fr
Gautier Dakin                 gautier.dakin at gmail.com
Roland Duclous            roland.duclous at gmail.com
Mehdi Khalloufi                mehdi.khalloufi at mines-paristech.fr
Pierre-Arnaud Raviart      pa at raviart.com
Frederic Coquel      frederic.coquel at cmap.polytechnique.fr
Dietmar Kroener      dietmar at mathematik.uni-freiburg.de 



How to come to the Laboratoire Jacques-Louis Lions

Hotels near the University Pierre et Marie Curie


EARLIER WORKSHOPS “Micro-Macro Modeling and Simulation of Liquid-Vapor Flows”

Tenth Workshop, Freiburg, February 2015

Ninth Workshop, Paris, February 2014

Eight Workshop, Berlin, February 2013

Seventh Workshop, Paris, February 2012

Sixth Workshop, Stuttgart, January 2011

Fifth Workshop, Strasbourg, April 2010

Fourth Workshop, Aachen, February 2009

Third Workshop, Strasbourg, January 2008

Second Workshop, Bordeaux, November 2007

Opening Workshop, Kirchzarten, November 2005