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#### Workshop 2016

#### “Modeling and Computation of Shocks and Interfaces”

#### Laboratoire Jacques-Louis Lions

#### Université Pierre et Marie Curie, Paris

*Organizers*

#### Philippe G. LeFloch (Paris)

#### Charalambos Makridakis (Brighton)

#### Supported by the ModCompShock ITN project

#### and a project PICS CNRS

#### Dec. 6 around 1:30pm to Dec. 8 around 1pm

#### Main speakers

#### Remi Abgrall (Zurich)

#### Benjamin Boutin (Rennes)

#### Christophe Chalons (Versailles)

#### Sergey Gavrilyuk (Marseille)

#### Charalambos Makridakis (Brighton)

#### Pierangelo Marcati (L’Aquila)

#### Siddhartha Mishra (Zurich)

#### Carlos Pares (Malaga)

#### Nils Risebro (Oslo)

#### Giovanni Russo (Catania)

#### Lev Truskinovsky (Palaiseau)

#### Titles of the lectures

**Benjamin Boutin **Numerical boundary layers for linear hyperbolic IBVP and semigroup estimate

**Christophe Chalons **On the computation of non conservative products and cell averages in finite volume methods

**Makridakis Charalambos** ** **Energy/entropy consistent computational methods

**Sergey Gavrilyuk** Shock-droplet interaction via a new hyperbolic phase field model

**Pierangelo Marcati** Splash singularities for incompressible viscoelatic fluids

**Siddhartha Mishra **Statistical solutions of systems of conservation laws

**Carlos Pares** Entropy stable schemes for degenerate convection-diffusion equations

**Nils Risebro** Numerical methods for scalar conservation laws with a stochastically driven flux

**Giovanni Russo** Shock capturing schemes for all Mach number flow in gas dynamics

**Lev Truskinovsky** Solitary waves in the FPU lattice: from quasi-continuum to anti-continuum limit

#### Schedule of the workshop

**Tuesday afternoon**

2pm-2:45pm: C. Makridakis

2:45-3:30pm: C. Pares

3:30pm: coffee break

4pm-4:45pm G. Russo

**Wednesday morning**

10am-10:45am: S. Gavrilyuk

10:45am: coffee break

11:15am: C. Chalons

Noon: lunch buffet

**Wednesday afternoon**

2pm-2:45pm R. Abgrall

2:45pm-3:30pm S. Mishra

3:30am coffee break

4pm L. Truskinovsky

**Thursday morning**

9:30am-10:15am N. Risebro

10:15am coffee break

10:45am B. Boutin

11:30am P. Marcati

12:15 lunch buffet (end of the workshop)

#### Participants to the workshop

- Remi Abgrall (Zurich) remi.abgrall at math.uzh.ch
- Benjamin Boutin (Rennes) chalons at math.jussieu.fr
- Christophe Chalons (Versailles) chalons at math.jussieu.fr
- Yangyang Cao (Paris) caoyangyang0721 at 163.com
- Marco De Lorenzo (Paris) marco.de-lorenzo at edf.fr
- Christian Dickopp (Aachen) dickopp at web.de
- Alain Forestier (Saclay) alain.forestier at cea.fr
- Sergey Gavrilyuk (Marseille) sergey.gavrilyuk at univ-amu.fr
- Maren Hantke (Magdeburg) maren.hantke at ovgu.de
- David Iampetro (Marseille) david.iampietro at edf.fr
- Philippe G. LeFloch (Paris) contact philippelefloch.org
- Charalambos Makridakis (Brighton) C.Makridakis at sussex.ac.uk
- Pierangelo Marcati (L’Aquila) pierangelo.marcati at gssi.infn.it
- Christoph Matern (Magdeburg) christoph.matern at ovgu.de
- Siddhartha Mishra (Zurich) siddhartha.mishra at sam.math.ethz.ch
- Roberto Molina (Paris) rmolina.sep at gmail.com
- Hieu Nguyen (Aachen) nguyen at instmath.rwth-aachen.de
- Carlos Pares (Malaga) pares at anamat.cie.uma.es
- Yohan Penel (Paris) penel at ann.jussieu.fr
- Chaoyu Quan (Paris) quanchaoyu at gmail.com
- Pierre-Arnaud Raviart (Paris) pa at raviart.com
- Nils Risebro (Oslo) nilshr at math.uio.no
- Giovanni Russo (Catania) russo at dmi.unict.it
- Lev Truskinovsky (Palaiseau) trusk at lms.polytechnique.fr
- Shugo Yasuda (Hyogo) yasuda at sim.u-hyogo.ac.jp
- Dimitrios Zacharenakis (Stuttgart) zachards at mathematik.uni-stuttgart.de

#### Other practical informations

The workshop will take place in the main lecture room 309 of the Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, which is located in the building 15-16.

Address: 4 Place Jussieu, 75258 Paris. Subway station: Jussieu.

List of hotels in the vicinity of the university

*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*

*____________________________*

**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)

#### ____________________________

**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

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### 9th DFG–CNRS WORKSHOP

### Micro-Macro Modeling and Simulation

### of Liquid-Vapor Flows

##### organized with financial support from DFG and CNRS

#### ____________________________

**Tuesday February 25, 2014 at 1:30pm **

**to **

**Thursday February 27, 2014 at 1:00pm**

____________________________

### 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****Schedule and abstracts here !**

____________________________

**INVITED SPEAKERS**

**Boris Andreaino**v (Besançon and Paris)

*On quasi-Richards equation and finite volume approximation of two-phase flow with unlimited air mobility*

**Robert Eymard**(Marnes-la-Vallée)

*Some convergence results for numerical schemes approximating two phase flow in porous media*

**Jan Giesselmann**(Stuttgart)

*A posteriori analysis of a discontinuous Galerkin scheme for a diffuse interface model*

**Philippe Helluy**(Strasbourg)

*Two-fluid pressure laws and non-convex hyperbolic domains (joint with J. Jung)*

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CONTRIBUTING SPEAKERS

CONTRIBUTING SPEAKERS

#### ____________________________

Main organizer

Philippe G. LeFloch (Paris)

Co-organizers

Benjamin Boutin (Rennes)

Frédéric Coquel (Palaiseau)

#### ____________________________

**PRACTICAL INFORMATIONS **

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”**

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

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## Seminar on

**Mathematical General Relativity**

*Organizers:*

* *Philippe G. LeFloch *(Paris) *

*Ghani Zeghib (Lyon)*

**ANR Project**

#### “Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

**Friday December 21, 2012**

### Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

**Lecture room ** 1525-3-21

**Lecture room**

**Speaker**

**11h15 – José A. Font (Valencia) Simulations of neutron star mergers and black hole-torus systems**

Abstract. Merging binary neutron stars are among the strongest sources of gravitational waves and have features compatible with the events producing short–hard gamma-ray bursts. Numerical relativity has reached a stage where a complete description of the inspiral, merger and post-merger phases of the late evolution of binary neutron star systems is possible. This talk presents an overview of numerical relativity simulations of binary neutron star mergers and the evolution of the resulting black hole–torus systems. Such numerical work is based upon a basic theoretical framework which comprises the Einstein’s equations for the gravitational field and the hydrodynamics equations for the evolution of the matter fields. The most well-established formulations for both systems of equations are briefly discussed, along with the numerical methods best suited for their numerical solution, specifically high-order finite-differencing for the case of the gravitational field equations and high-resolution shock-capturing schemes for the case of the relativistic Euler equations. A number of recent results are reviewed, namely the outcome of the merger depending on the initial total mass and equation of state of the binary, as well as the post-merger evolution phase once a black hole–torus system is produced. Such system has been shown to be subject to non-axisymmetric instabilities leading to the emission of large amplitude gravitational waves.

** **

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## 7th DFG–CNRS WORKSHOP

## Two-Phase Fluid Flows. Modeling and Computational Methods

*Main organizer: *

* *Philippe G. LeFloch (Univ. Pierre et Marie Curie, Paris)

#### Co-organizers:

#### Christophe Berthon (Nantes) and Philippe Helluy (Strasbourg)

#### With financial support from the DFG and the CNRS

**Tuesday Feb. 14, 2012 at 2pm to Thursday Feb. 16 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***SCHEDULE, list of participants, and abstracts*

**INVITED SPEAKERS**

(Berlin)

Gonca Aki

*An incompressible diffuse flow with phase transition*

**Mathieu Bachmann** (Aachen)* Numerical simulation of shock wave-bubble interactions using laser-induced cavitation bubbles*

**Frank Boyer** (Marseille) * Numerical methods for a three-component phase field model*

**Sergey L. Gavrilyuck** (Marseille) *Diffuse interface model for compressible fluid-compressible elastic-plastic solid interaction*

**Maren Hantke** (Magdeburg) *Exact solutions to the Riemann problem for compressible isothermal Euler equations for two phase flows, with and without phase transition*

**Jonathan Jung **(Strasbourg) *Computing bubble oscillations on GPU (graphics processing unit)*

**Mirco Kraenkel **(Freibur*g) Numerics for phase field models*

**Hélène Mathis **(Nantes) *Model adaptation for hyperbolic systems with relaxation *

**Khaled Saleh **(Paris)* A splitting method for the isentropic Baer-Nunziato two-phase flow model *

**Nicolas Seguin** (Paris) * Model adaptation in hierarchies of hyperbolic systems*

**Gabriele Witterstein** (Munich) *Existence of transition profiles for compressible flows*

Christophe Zeiler (Stuttgart) Curvature driven liquid-vapor flow of compressible fluids

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**PRACTICAL INFORMATIONS **

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-Vapour Flows”**

Sixth Workshop, Stuttgart, Jan. 2011

Fourth Workshop, Aachen, Feb. 2009

Second Workshop, Bordeaux

Opening Workshop, Kirchzarten, Nov. 2005