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

*organized with the financial support of*

*DFG, CNRS, and ITN*

**Wednesday March 2nd, 2016** (afternoon)

**Wednesday March 2nd, 2016**(afternoon)

**to ****Friday March 4th, 2016** (at noon)

**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*

*Lecture room 15-16 — 309*

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**INVITED SPEAKERS**

**Nina Aguillon** (Paris)

**Nina Aguillon**

**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)

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**Main organizer**

**Philippe G. LeFloch (Paris)**

**Co-organizers**

**Dietmar Kroener (Freiburg)**

**Frédéric Coquel (Palaiseau)**

**SCHEDULE**

__Wednesday afternoon__*(Chairman P.G. LeFloch)*

**Robert Eymard**

**(**Marne-La-Vallée)

**Jan Giesselman**(Stuttgart)

*Coffee break*

**Philippe Helluy**(Strasbourg)

**Mirko Kraenkel**(Freiburg)

__Thursday morning__*(Chairman*

*Jan Giesselman)*

**Christophe Berthon**(Nantes)

**Johannes Daube**(Freiburg)

*Coffee break*

**Christophe Chalons**(Versailles)

**Dietmar Kroener**(Freiburg)

*Lunch break*

**Thursday afternoon***(Chairman F. Coquel)*

**Bruno Després**(Paris)

**Arnold Reusken**(Aachen)

*Coffee break*

**Nina Aguillon**(Paris)

**Rüdiger Müller**(Berlin)

__Friday morning__*(Chairman D. Kroener)*

**Carlos Pares**(Malaga)

**Florence Drui**(Châtenay-Malabry)

**Christian Dickopp**(Aachen)

**Frédéric Coquel**(Palaiseau)

**Nina Aguillon**(Paris)

__Numerical approximation of hyperbolic systems containing an interface__

**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

**Christian Dickopp**(Aachen)

__Coupling of (elastic)-plastic solids with compressible two-phase fllows for cavitation damaging__

**Florence Drui**(Châtenay-Malabry)

__A hierachy of homogeneous two-fluid models and numerical methods for simulating various regimes of two-phase flows__

**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.__

**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__

**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**

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**PRACTICAL INFORMATIONS **

How to come to the Laboratoire Jacques-Louis Lions

Hotels near the University Pierre et Marie Curie

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**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