Born 1 June 1968 in Trier (Germany)
French citizen
Married, three children (22, 19 and 11)
7 rue des peupliers,
67117 Furdenheim,
France
+33 3 88 21 11 05 or +33 6 81 50 65 80
IRMA, UMR CNRS 7501,
7 rue Descartes,
67000 Strasbourg,
France
+33 3 68 85 02 01
http://wwwirma.ustrasbg.fr/∼helluy
https://scholar.google.fr/citations?user=x56VAMYAAAAJ&hl=fr
philippe.helluy@unistra.fr
I am interested in mathematical and numerical modeling for physics. My research is often related to industrial problems and to High Performance Computing (HPC).
I did my PhD in Toulouse on numerical methods for electromagnetism: boundary integral equations and Discontinuous Galerkin (DG) methods. When I moved to Toulon, I had the opportunity to work on computational fluid dynamics with applications to NavierStokes and multiphase flows. More recently I have done research on numerical methods for plasma physics: MagnetoHydroDynamics (MHD) and VlasovMaxwell models.
Since my PhD I’ve taught in various fields of physics, mathematics and computer science to future engineers or mathematicians, at the Licence or Master levels. Like most of French university professors I usually teach about 200 hours a year. I benefited from a CNRS sabbatical in 2006 (100 hours of teaching instead of 200) and a Strasbourg University sabbatical in 2013 (100 hours of teaching instead of 200).
Here is a nonclosed list of examples of given lectures:
Start  End  Activity  Location 
Sept. 1985  July 1987  “Classes préparatoires”, mathematics.  Lycée Hoche, Versaille 
Sept. 1987  July 1990  Aeronautics and space engineering studies.  Sup’aéro, Toulouse 
Sept. 1990  July 1990  Master, applied mathematics.  Université Paul Sabatier, Toulouse 
Sept. 1990  Aug. 1993  PhD, thesis “Numerical resolution of harmonic Maxwell equations by a Discontinuous Galerkin method. Application to RADAR cross section”. electromagnetism, applied mathematics, scientific computing. Advisor: PierreAlain Mazet.  ONERA (French national aerospace research institute), Toulouse 
Sept. 1990  Aug. 1993  PhD Teaching assistant (“moniteur”). 64 hours teaching per year: Sup’aéro, ENSICA (engineering schools) and Université Paul Sabatier (math. students)  Sup’aéro, ENSICA and Université Paul Sabatier, Toulouse 
Sept. 1993  Aug. 1994  Temporary Assistant Professor in mathematics (ATER)  Université Paul Sabatier, Toulouse 
Sept. 1994  Aug. 2006  Permanent Assistant Professor at the engineering school in Toulon University (ISITV: “Institut des Sciences de l’Ingénieur de Toulon et du Var”)  Université de Toulon et du Var (UTV) 
Jan. 2005  Jan. 2005  Habilitation thesis “Numerical simulation of multiphase flows: from theory to practice”. Advisor: Thierry Gallouët.  Université de Toulon et du Var (UTV) 
Sept. 2006  now  Full Professor at “Institut de Recherche Mathématique Avancée”, IRMA UMR CNRS 7501. First class since October 2012.  Université de Strasbourg (UDS) 
After aeronautics engineering studies, I did my PhD under the supervision of PierreAlain Mazet at the French aerospace research agency (ONERA) in Toulouse. I worked on numerical simulations of RADAR cross sections. I developed an original parallel method for coupling boundary integral equations and a Discontinuous Galerkin (DG) method.
In 1994 I moved to a permanent Assistant Professor position in the University of Toulon, at the engineering Institute (ISITV: “Institut des Sciences de l’Ingénieur de Toulon et du Var” now called “SeaTech” since 2014). In Toulon, my main research subject was the mathematical and numerical modeling of compressible multiphase flows. With several collaborators I developed new finite volume methods based on entropy optimization principles. Those methods were implemented in parallel software and applied to flows with phase transitions, wave breaking simulations, internal ballistics of guns. As I was in Toulon, I also worked on theoretical aspects of the NavierStokes equations. I also made a series of papers on inverse problems in ocean geoacoustics.
I passed my habilitation thesis in 2005 and was hired in 2006 on a full professor position in the University of Strasbourg. I continue to work on mathematical and numerical modeling of multiphase flows. I also tackled new subjects concerning plasma physics modeling and software implementation on new computer architectures with hybrid CPU/GPU computing.
In this paragraph I present shortly a few of my favorite former works.
In this work [8] with Thomas Barberon and Sandra Rouy, we studied a compressible gasliquid flow occurring in a submarine missile ejection device. We applied a fully Eulerian finite volume method able to track naturally the liquidgas interface. For obtaining correct results it is necessary to adapt carefully several techniques: contact preserving schemes, timedependent boundary condition that change of type, local time stepping. We were then able to reproduce precisely actual experiments. On Figure 1 the liquidgas interface can be seen at different times.
I used the same kind of approaches for computing wave breaking. See http://www_irma.u_strasbg.fr/~helluy/soliton.htm.
In order to improve the modeling, we extended the approach in [9] in order to take into account the vaporization (cavitation process) that arises in the liquid due to violent pressure drop. This improved method is based on a finite volume method with a relaxation source term constructed from an entropy optimization principle. An interesting point of the paper is that applying directly the liquidvapor pressure law is not a correct approach because there exists a continuous family of entropy solutions. Different solutions can be obtained by changing the CFL number of the simulation. With the entropy optimization approach we recover the physical solution, which has a maximal entropy dissipation rate.
I continue to work in Strasbourg on interface capturing method. In [10] I developed with Jonathan Jung a new fully conservative and stable finite volume approach for computing very stiff gasliquid problems without pressure oscillations at the gasliquid interface. To my knowledge, this is the only finite volume scheme that is both conservative and stable on these kinds of problems. It is based on a ALE approach with a random remap step.
In [28] we studied a compressible multiphase flow made of a solid and a gas phase. Each phase has its own velocity. The objective is to model the grain combustion inside a gun (internal ballistics). Some models suppose that the gas pressure p_{g} of the gas and the solid pressure p_{s} are linked by a pressure equilibrium relation of the form
where R > 0 is the granular stress. Generally, those models are not hyperbolic and thus unstable. Some authors have proposed models with pressure evolution equations for each phase and a relaxation source term in order to recover the pressure equilibrium.
In our work, we perform a rigorous analysis of this relaxation model, give an analytic form for the granular stress that ensures entropy dissipation. We also apply the model to an actual gun and compare it with another model.
The Legendre transform is a theoretical tool that is used in many fields of mathematics and physics. For a convex function f the Legendre transform is defined by
There is a beautiful analogy between the Legendre transform and the Fourier transform in the theory of the (max,+) algebra. Indeed, if we consider the two following operations
it is possible to draw the following equivalence between classical analysis and (max,+) analysis.
classical analysis  (max,+) analysis 
a ⋅ b  a ⊙ b = a + b 
a + b  a ⊕ b = max(a,b) (a ⊕ a = a) 
∫ _{Ω}f(x)dx  f(x) = f(x) 
characters: χ(s,x + y) = χ(s,x) ⋅ χ(s,y)  χ(s,x + y) = χ(s,x) ⊙ χ(s,y) 
χ(s,x) = exp(−isx)  χ(s,x) = s ⋅ x 
Fourier: (s) = ∫ f(x)exp(−isx)dx  Legendre: f^{∗}(s) = f(x) ⊙ χ(s,x) = sx + f(x) 
Convolution: (f ∗ g)(x) = ∫ _{y}f(x − y)g(y)dy  Supconvolutionf□g(x) = f(x − y) + g(y) 
(f ∗ g)^{∧} = ⋅ĝ  (f□g)^{∗} = f^{∗}⊙ g^{∗} = f^{∗} + g^{∗} (f,g concave usc) 
A consequence of this analogy is that it is possible to construct a fast algorithm, similar to the fast Fourier transform, for computing Legendre transform and supconvolution of sampled functions.
In [11] we apply the above theory to the thermodynamics of mixture. We consider a mixture of two components i = 1,2 characterized by their energy laws ε_{i}(ρ,σ), function of the density ρ and entropy σ. In the Legendre formalism the dual variables of ρ and σ are the chemical potential μ and the temperature θ. The pressure p_{i}(μ,θ) is then the Legendre transform of ε_{i}(ρ,σ). After a miscible mixture of the two components, the pressure and energy are given by
where □ denotes the supconvolution operation. For an immiscible mixture the relations become
where co(f) denotes the convex envelope of f.
It is much easier to compute max and + operations than supconvolutions or convex envelopes. Therefore, we propose an algorithm, based on the fast Legendre transform, in order to compute in an efficient way, the mixture equation of state from tabulated laws of each component. We apply the method to phase transition and to mixture of reactive gases.
Since 2009 I generally implement my software using the OpenCL library. OpenCL is a programming framework, similar to CUDA in order to address GPU or multicore accelerator in a unified way.
In [23] with Anaïs Crestetto we have coupled a ParticleInCell (PIC) method and a Discontinuous Galerkin (DG) method for VlasovMaxwell simulations. The method is implemented on GPU with OpenCL. It is applied to the numerical simulation of a medical Xray generator. With our software, we were awarded a prize at the AMD OpenCL innovation challenge in 2011 https://community.topcoder.com/amdapp/
With Jonathan Jung I also applied multiGPU computing on the scheme that we developed in [39]. With OpenCL accelerations, we were able to compute test cases on very fine meshes (an example of a liquidshock interaction is shown on Figure 2)
For addressing more computational power it becomes almost mandatory to follow a task graph approach. The method consists in splitting the whole simulation into several elementary computational tasks with their dependencies. The tasks are then distributed automatically at runtime on the available resources for efficient parallel computations. This approach is described in [49], where we develop our own homemade runtime system, and apply it to electromagnetic simulations. More recently, we switched to a more general environment, developed by Inria specialists for more than ten years: StarPU. It is a runtime system for distributing the tasks on hybrid accelerators (CPU and GPU). The results are not yet published but are described in the thesis of Michel Massaro (Chapter 5):
https://tel.archives_ouvertes.fr/tel_01410049
NavierStokes theory In this paper [12] written with F. Golay, we prove a rigorous mathematical result of existence and uniqueness for weakly compressible NavierStokes equations. The proof is based on an abstract fixed point method in Sobolev spaces. The fixed point approach can also be applied numerically. The resulting scheme is not very efficient but I like it anyway because the fixed point algorithm requires to solving three different types of PDE with adapted Finite Element (FE) methods: a Laplace equation solved by standard finite elements, a transport equation, which we solved with the SUPG approach, and a Stokes problem that we solved with CrouzeixRaviart elements. This was a good exercise for learning about the FE method.
In the end, we were able for instance to evaluate the contraction constant of the theoretical fixed point method (see Figure 3).
Inverse problems in ocean geoacoustics In [15] we use an optimal control technique for identifying the acoustic characteristics of the submarine ground from measurements. The method is applied to a popular reduced acoustic model in ocean engineering: the paraxial Tappert model, which has the same mathematical structure as the Schrödinger equation. See Figure 4 where an example of the reconstruction process is presented.
In this table I give the list of the thesis that I supervised. The indicated rate has no administrative meaning. It is an indication of my actual investment in the thesis supervision.
Name  Rate 
Institution/cosupervisor 
subject 
defense 
present position 


Thomas BARBERON  90% 
Univ. Toulon/ M.C. Pélissier 
Numerical simulation of compressible flows with phase transition 
December 2002 
General Manager at TMH Offshore Engineering Kuala Lumpur, Malaysia 
Anaïs CRESTETTO  70% 
UDS, É. Sonnendrücker 
Numerical simulation for plasma physics 
October 2012 
Assistant professor Nantes University 
Pierre GERHARD  50% 
UDSRégion Alsace/L. Navoret 
Kinetic methods for acoustics. Application to room acoustic numerical modeling. 
2018 

Pierre GLANC  10% 
UDS, M. Mehrenberger 
SemiLagrangian numerical methods for plasma physics 
January 2014 
Postdoc, ENS Lyon 
Conrad HILLAIRET  50% 
UDS, E. Franck 
LatticeBoltzmann approaches for magnetohydrodynamics 
2019 

Jonathan JUNG  80% 
UDS, J.M. Hérard 
Compressible Multiphase flows, GPU simulations 
October 2013 
Assistant Professor University of Pau 
Yujie LIU  10% 
EDF Paris, J.M. Hérard 
Water hammer simulation in nuclear plants pipes. 
September 2013 
Assistant Professor Sun Yatsen. School of Data and Computational Science 
Juan MARTINEZ  10% 
LABEX IRMIA, UDS, P. Clauss 
Automatic compilation. Application to scientific software. Collaboration with computer scientists. 
September 2016 
Software research engineer, Lyon. 
Michel MASSARO  70% 
LABEX IRMIA, UDS, V. Loechner 
Magnetohydrodynamics, astrophysics. Hybrid CPU/GPU computing. Collaboration with computer scientists and astrophysicists 
December 2016 
Temporary research engineer, AxesSim. 
Hélène MATHIS  90% 
EDF Paris/J.M. Hérard 
Thermodynamics of multiphase flows. Numerical methods for hyperbolic systems. 
September 2010 
Assistant professor, University of Nantes 
Julien NUSSBAUM  80% 
ISL/EDF/J.M. Hérard 
Numerical simulation of internal ballistics of guns. Multiphase and granular flows. 
November 2007 
R&D Structural Mechanics Engineer, Ansaldo Energia Switzerland 
Nhung PHAM  50% 
UDS, L. Navoret 
Reduction methods for Vlasov equation and plasma physics. 
December 2016 
Temporary assistant professor, Strasbourg 
Sandra ROUY  80% 
Univ. Toulon/ M.C. Pélissier 
Numerical simulation of compressible airwater flows 
December 2000 
Associate head of scientific community Sopra (software engineering) 
Lauriane SCHNEIDER  10% 
UDS, G. Schäfer 
Numerical simulations of geophysical flows 
February 2015 
Preparation of teacher exams UDS 
Thomas STRUB  100% 
CIFRE, AxesSim company Illkirch 
Numerical simulations for electromagnetism on GPU 
March 2015 
Permanent research engineer at AxesSim 
Bruno WEBER  70% 
AxesSim/ 
Optimization of hybrid CPU/GPU simulations for electromagnetism. Interaction with the human body. 
2018 






With Anaïs Crestetto I was awarded the fourth prize at the AMD OpenCL innovation challenge 2011: “Numerical simulation of a medical Xray generator on GPU:
https://community.topcoder.com/amdapp/
Here is a nonexhaustive list of present and former collaborations (the PhD students are listed in the above table).
I was coorganizer of several workshops and conferences. For instance:
I am regularly invited to conferences, workshops or summer schools. For instance:
Over the years I made reviews for various journals. For instance: Math Reviews, M2AN, M3AS, Computers and Fluids, SIAM Journal on Numerical Analysis, Journal of Computational Physics, International Journal for Numerical Methods in Fluids, IJNMF, Journal of Mechanical Science and Technology, ESAIM, Oil & Gas Science and Technology, Numerical Methods for Partial Differential Equations, International Journal of Offshore and Polar Engineering (!), SIAM Journal on Applied Mathematics, CRAS, etc.
I am associate editor of the International Journal of Finite Volumes: http://www.i2m.univ_amu.fr/IJFV/
Regularly I write reviews on PhD or habilitation thesis or on for research project calls: CNRS calls on mathematics and physics, ANR (French research agency), US Army, French regions calls, etc.
When I arrived in Strasbourg in 2006, Eric Sonnendrücker was head of an Inria projectteam CALVI (CALcul scientifique et VIzualization). In 2012 he obtained a position in Garching at the MaxPlanckInstitut für Plasmaphysik.
I became head of CALVI. See https://www.inria.fr/en/teams/calvi .
I submitted a new project after the final evaluation of CALVI in 2013. The new project TONUS (TOkamak NUmerical Simulation) was accepted in 2014. See https://www.inria.fr/en/teams/tonus.
As of December 2016, TONUS is composed of the following permanent researchers:
Postdoc researchers: David Coulette, Laura Mendoza.
PhD: Nicolas Bouzat, Ksander Ejjaaouani, Pierre Gerhard, Conrad Hillairet, Michel Massaro, Nhung Pham, Bruno Weber.
This project is related to the construction in France of the International Thermonuclear Experimental Reactor (ITER). This international project aims at producing thermonuclear fusion reactions in a hot hydrogen plasma (temperature≃ 150 × 10^{6}K). In the long term it might become a way to produce clean energy.
The plasma is confined with strong magnetic fields in a doughnutshaped device: a tokamak. The main mathematical model for computing the plasma evolution is the Vlasov equation. Its unknown is the distribution function f(x,v,t) that counts the number of ions at point x and time t having velocity v. The problem is timedependent in a sixdimensional phase space. The Vlasov equation reads
where B is the given magnetic field imposed by the tokamak superconducting coils, Φ is the electric potential, solution of the Poisson equation
and C(f) is a collision source term. This simple mathematical model leads to interesting mathematical problems: asymptotic limits for strong magnetic fields, large or small collision rates, etc.
Because it is set in a highdimensional phase space, it is also a challenge for HPC. It requires the full power of the biggest supercomputers for obtaining realistic simulations.
In TONUS, we have obtained new results on the mathematical analysis of plasma models.
We have also proposed new numerical schemes for plasma physics.
CALVI and now TONUS are the advocates of semiLagrangian methods for solving kinetic equations. The methods are implemented in the Selalib library, which is a joint software project between Inria and the MaxPlanckInstitut für Plasmaphysik in Garching. The most efficient semiLagrangian methods are generally transferred into GYSELA the production code of CEA (French atomic agency) for tokamak simulations.
For more details, we refer to the web pages of CALVI and TONUS and to the series of annual reports:
We also refer to the web page of Selalib http://selalib.gforge.inria.fr.
More recently, in order to handle more complex geometry, we have started to develop DG solvers for the Vlasov equations. The new developments are included in SCHNAPS the other main software project of the TONUS team:
http://schnaps.gforge.inria.fr
Since my PhD I teach in various fields of physics, mathematics and computer science to future engineers or mathematicians. Here is a nonclosed list of examples:
Here are some links (generally in French, but in English sometimes) with teaching material for students:
In this section I give two examples of teaching sessions at the master level.
In this session I propose to the students to compute a simplified model of sugar dissolution in the morning coffee. The sugar concentration u(x,t) depends on space variable x ∈ [0,L] and time t ∈ [0,T]. It is a solution of the diffusion equation with initial and boundary conditions
−  = 0,  
u(x,0)  = u_{0}(x),  
(0,t) = (L,t)  = 0. 
The plan of the lecture is then the following:
The lecture can be adapted to the knowledge of the students. For instance, for math students it is possible to go further on some points: convergence of the Fourier series, convergence study of the finite difference scheme, rigorous proof of stability. For physics students I would reintroduce the physical constants in the model...
In practice I have observed that the students have problems with the programming part. They need time to program in a correct way, without bugs and with adequate validations the Fourier series method, the LU solver and the finite difference method. It is possible to go faster by programming the method into Matlab (or Matlab clone like Octave or Scilab). However it is less interesting on the pedagogical side, because programming in C or FORTRAN generally leads to a better understanding of how computers work.
Other examples of teaching sessions (in French) can be found here:
http://www_irma.u_strasbg.fr/~helluy/CS/cs.html
In the second year of master I generally give lectures on optimal control. For instance, one session is devoted to answering the following question: how to place the heaters in a room in order to obtain the most uniform temperature ?
The problem can be modeled in the following way: the room is noted Ω. The way to heat the room is the control u. In the room, the temperature T_{u}(x) is a solution of the stationary heat equation
On a part of the room boundary Γ_{d} there is a (badly insulated) window where we apply Dirichlet condition
On the rest of the boundary Γ_{n} we apply the control (a heat flux)
We want the temperature to be close to a constant desired temperature
(for instance Θ = 20°C). We thus consider the cost function
The parameter ϵ > 0 is a small parameter that will ensure the uniqueness of the control u. In practice it can also be used to adjust the level of energy saving (if ϵ is large, the solution is u ≃ 0, which corresponds to no heating at all).
I explain then to the students how to compute the gradient of the cost function J with the aid of the adjoint state theory. Then the students program a gradient or a conjugate gradient method to solve the optimal control problem. The computations are made in the Freefem++ software (http://www.freefem.org). This software allows to implement in a very easy way various finite element variational methods.
Other optimal control studies (in French) are proposed here: http://www_irma.u_strasbg.fr/~helluy/copt/copt.htm
In my career I developed numerical methods that have been implemented in various software projects.
It is a finite volume software written in C++ for solving the gaswater inside a submarine gas generator. The flow is solved by the finite volume method in axisymmetric geometry with special tricks for handling liquidgas interface, boundary conditions and local timestepping (see section 1.2.1). The software was sold to DCN (“Direction des Construction Navales”, French navy industry) in 2000.
CM2 is a parallel FORTRAN software for computing 3D multifluid flows. It is used for instance for wave breaking simulations. It contains other models for computing flows with phase transitions, MHD flows with high order local timestepping.
EOLENS is a modification of CM2 which contains additional k − ϵ turbulence models. It was sold in 2006 to the PRINCIPIA company.
DIWA it is a research software for solving VlasovMaxwell equations by a ParticleInCell (PIC) and a Discontinous Galerkin (DG) methods. It was written with Anaïs Crestetto. It uses the OpenCL library for addressing GPU acceleration. It was used for simulating a medical Xray generator. The principle is to create a strong electromagnetic field that will extract and accelerate electrons from the cathode. When the electrons hit the anode they produce Xrays. The software was awarded a prize at an AMD OpenCL international competition in 2011.
A video demonstrating the acceleration offered by the GPU, the evolution of the electromagnetic field and electrons can be seen at:
https://www.youtube.com/watch?v=R7jXW4oXHDI
The video was created by using the possibilities of OpenCL to create on the fly OpenGL visualizations (in other words, the video card is computing, creating OpenGL images and capturing itself at the same time !)
CLBUBBLE is also a research OpenCL software. It implemented the method described in [39] for solving gasliquid compressible flows. A video demonstrating a shockbubble interaction can be seen at:
https://www.youtube.com/watch?v=c8hcqihJzbw
For creating a fast video the mesh resolution is rather coarse. It is possible to run CLBUBBLE on much finer meshes and with several GPUs (see section 1.2.1).
In developing the two previous research programs, we obtain good GPU accelerations. However, in the multiGPU simulation we realize that it is very important to send the computation and memory transfer tasks in an asynchronous way. In addition, on a supercomputer node it is generally possible to access several GPU and multicore CPU. For efficiency it is thus important to launch operations on both architectures (hybrid computing). It becomes difficult to handle the task dependencies directly and therefore very important to use a runtime system. I decided to use StarPU http://starpu.gforge.inria.fr. StarPU is a runtime system library developed at Inria Bordeaux since 2006. It allows to describing the computational task in a more abstract way. The programmer has to split its simulation into several computation tasks. For each task he describes the data dependency: read, write or read/write mode. This is the dataflow paradigm. Each task can be programmed in several different ways (CPU, GPU, CUDA, OpenCL, etc.). The tasks are submitted in a correct order to StarPU. The runtime system then distributes them in parallel on the available resources in the most efficient way.
SCHNAPS (“Solveur Conservatif Hyperbolique Nonlinéaire Appliqué aux PlaSmas”) is a research software project developed in my team for handling this kind of hybrid computing approach. http://schnaps.gforge.inria.fr. SCHNAPS is a generic solver for conservation laws.
CLAC is an industrial version of SCHNAPS with specific models developed for electromagnetic simulations. It is developed in collaboration with the software company AxesSim in Strasbourg. One of the objectives is to develop numerical tools for simulating electromagnetic objects (antenna, smartphones, captors) near to the human body: http://www.axessim.eu/category/news/
In my career I participated to the collective life of my universities. Here is also a nonclosed list of examples:
Here is a list of some supports that I obtained for my research projects.
In my career I had several occasions to realize applied research contracts with industry or less academic institutions:
In 1998 with Vincent Rey I realized a short engineering study for modeling waves in the harbor of Banyuls. The results are described here (in French): http://www_irma.u_strasbg.fr/~helluy/ADMIN/CV/BANYULS.pdf
In 19972000 I made a software study for DCN (“Direction des Constructions Navales”, French navy submarine industry) for simulating a submarine gas generator. The contract (around 100 k€) permits to support the PhD grant of Sandra Rouy. The resulting software DIVAXI (see section 4.1) was sold to DCN.
in 2006 I made a software study of 30k€ for the PRINCIPIA company in La Ciotat. PRINCIPIA is a subsidiary of AREVA specialized in software modeling for industry. With Frédéric Golay we developed a finite volume compressible k − ϵ turbulent module in EOLENS, a PRINCIPIA software.
AxesSim is a software company in Strasbourg, specialized in electromagnetic simulations. http://www.axessim.eu.
Since 2012 I have a collaboration with AxeSim for accelerating Discontinuous Galerkin solvers on GPU. This collaboration permitted to support the PhD thesis of Thomas Strub and Bruno Weber and two accompanying contracts (220 k€ for 6 years). This collaboration is also supported by DGA (French defense agency) and BPI (French public bank for investment).
As explained in section 2.3 we have developed in Tonus very efficient numerical methods for solving kinetic equations. Recently, I have launched a research project with my team for harnessing kinetic solvers for general systems of conservation laws.
Indeed, I have recently realized that all conservative systems of conservation laws admit a minimalist kinetic interpretation. The kinetic formalism mimics the Boltzmann theory of gas. The ingredients of a kinetic model are the following:
 (1) 
When the relaxation time τ is small, the kinetic equation provides an approximation of the hyperbolic conservative system
with
The main idea is that numerical solvers for the linear scalar transport equation lead to natural solvers for the nonlinear hyperbolic system. This approach is very general and very fruitful for theoretical reasons. For instance, it permits to construct numerical fluxes with good mathematical properties for general finite volume methods.
The kinetic model can also be solved directly when the velocity space V is small, typically a lattice with a few points. With small velocity lattices, the method presents many advantages for parallelism, generic implicit solvers, stability, asymptotic properties, etc. The standard Lattice Boltzmann Method (LBM) consists in solving the transport equation (1) exactly with the characteristic method. Its main drawback is that this imposes Cartesian space grids and that the time step Δt is fixed by the gris step Δx. In the Discontinuous Galerkin LBM (DGLBM) the transport equation is solved with a Discontinuous Galerkin method. This is very interesting because then the time step is free, the mesh can be unstructured and the method can easily be made implicit without the actual resolution of a large linear system.
Two preprints on the DGLBM are available here:
https://hal.archives_ouvertes.fr/hal_01422922
https://hal.archives_ouvertes.fr/hal_01451393
In the next year, my main objective is to explore many aspects of the DGLBM methods and applications. Many questions arise and many software developments are needed:
In France we have a strong incitation to deposit our papers on the HAL repository. The full text of most of my publications (including PhD thesis, habilitation thesis and unpublished reports) can be found here: http://hal.archives_ouvertes.fr/aut/helluy/
See also my Google Scholar page: https://scholar.google.fr/citations?user=x56VAMYAAAAJ&hl=fr
[1] Philippe Helluy. Résolution numérique des équations de Maxwell harmoniques par une méthode d’éléments finis discontinus. PhD thesis, École nationale supérieure de l’aéronautique et de l’espace, 1994. https://hal.archives_ouvertes.fr/tel_00657828
[2] Philippe Helluy and Vincent Rey. Modélisation numérique de la houle dans le port de Banyuls. Technical report, Technical report, ISITV, 1998. Contrat de recherche avec la mairie de Banyulssurmer, 1998. http://www_irma.u_strasbg.fr/~helluy/ADMIN/CV/BANYULS.pdf
[3] Philippe Helluy. Simulation numérique des écoulements multiphasiques: de la théorie aux applications.". Habilitation thesis, Université de Toulon, 2005. https://hal.archives_ouvertes.fr/tel_00657839
[4] Philippe Helluy. A portable implementation of the radix sort algorithm in OpenCL. https://hal.archives_ouvertes.fr/hal_00596730, 2011.
[5] Christophe Steiner, Michel Mehrenberger, Nicolas Crouseilles, and Philippe Helluy. Quasineutrality equation in a polar mesh. https://hal.archives_ouvertes.fr/hal_01248179, 2015.
[6] Philippe Helluy. Stability analysis of an implicit lattice boltzmann scheme. https://hal.archives_ouvertes.fr/hal_01403759, 2016.
[7] David Coulette, Emmanuel Franck, Philippe Helluy, Michel Mehrenberger, and Laurent Navoret Palindromic discontinuous Galerkin method for kinetic equations with stiff relaxation. https://hal.archives_ouvertes.fr/hal_01422922, 2016.
[8] Thomas Barberon, Philippe Helluy, and Sandra Rouy. Practical computation of axisymmetrical multifluid flows. International Journal on Finite Volumes, 1:1–34, 2003. https://hal.archives_ouvertes.fr/hal_00139598
[9] Thomas Barberon and Philippe Helluy. Finite volume simulation of cavitating flows. Computers & fluids, 34(7):832–858, 2005. https://hal.archives_ouvertes.fr/inria_00071762
[10] Philippe Helluy and Jonathan Jung. Interpolated pressure laws in twofluid simulations and hyperbolicity. In Finite Volumes for Complex Applications VIIMethods and Theoretical Aspects, pages 37–53. Springer International Publishing, 2014. https://hal.archives_ouvertes.fr/hal_00957043
[11] Philippe Helluy and Hélène Mathis. Pressure laws and fast legendre transform. Mathematical Models and Methods in Applied Sciences, 21(04):745–775, 2011. https://hal.archives_ouvertes.fr/hal_00424061
[12] Frédéric Golay and Philippe Helluy. Numerical simulation of a viscous compressible fluid based on a splitting method. Séminaire de mathématiques de l’Université de Ferrare, Ferrare, http://www_irma.u_strasbg.fr/~helluy/ADMIN/CV/nastocomp.pdf 1998.
[13] JeanClaude Le Gac, Yann Stephan, Mark Asch, Philippe Helluy, and JeanPierre Hermand. A variational approach for geoacoustic inversion using adjoint modeling of a PE approximation model with non local impedance boundary conditions. In Theoretical and computational acoustics 2003, pages 254–263. World Sci. Publ., River Edge, NJ, 2004. http://www_irma.u_strasbg.fr/\~helluy/ADMIN/CV/acoustic2.pdf
[14] Christoph Altmann, Thomas Belat, Michael Gutnic, Philippe Helluy, Helene Mathis, Eric Sonnendruecker, Wilfredo Angulo, and JeanMarc Herard. A local timestepping discontinuous galerkin algorithm for the MHD system. In ESAIM: proceedings, volume 28, pages 33–54. EDP Sciences, 2009.
[15] Mark Asch, JeanClaude Le Gac, and Philippe Helluy. An adjoint method for geoacoustic inversions. In PICOF’02: problèmes inverses, contrôle et optimisation de formes. http://www_irma.u_strasbg.fr/\~helluy/ADMIN/CV/acoustic.pdf, pages 23–29, 2002.
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[17] Thomas Barberon and Philippe Helluy. Finite volume simulations of cavitating flows. In Finite volumes for complex applications, III (Porquerolles, 2002), pages 441–448. Hermes Sci. Publ., Paris, 2002.
[18] Françoise Bourdel, PierreAlain Mazet, and Philippe Helluy. Resolution of the nonstationary or harmonic Maxwell equations by a discontinuous finite element method. application to an emi (electromagnetic impulse) case. In 10th international conference on computing methods in applied sciences and engineering on Computing methods in applied sciences and engineering, pages 405–422. Nova Science Publishers, Inc. Commack, NY, USA, 1992.
[19] Frédéric Coquel, Thierry Gallouët, Philippe Helluy, JeanMarc Hérard, Olivier Hurisse, and Nicolas Seguin. Modelling compressible multiphase flows. In ESAIM: Proceedings, volume 40, pages 34–50. EDP Sciences, 2013.
[20] Frédéric Coquel, Philippe Helluy, and Jacques Schneider. Secondorder entropy diminishing scheme for the euler equations. International journal for numerical methods in fluids, 50(9):1029–1061, 2006.
[21] Clémentine Courtès, Emmanuel Franck, Philippe Helluy, and Herbert Oberlin. Study of physicsbased preconditioning with highorder galerkin discretization for hyperbolic wave problems. https://hal.archives_ouvertes.fr/hal_01401547, 2016.
[22] Anaïs Crestetto and Philippe Helluy. Multiwaterbag model and method of moments for the Vlasov equation. In Finite Volumes for Complex Applications VI Problems & Perspectives, pages 293–301. Springer Berlin Heidelberg, 2011.
[23] Anaïs Crestetto and Philippe Helluy. Resolution of the VlasovMaxwell system by PIC discontinuous galerkin method on GPU with OpenCL. In ESAIM: Proceedings, volume 38, pages 257–274. EDP Sciences, 2012.
[24] Anaïs Crestetto, Philippe Helluy, and Jonathan Jung. Numerical resolution of conservation laws with OpenCL. In ESAIM: Proceedings, volume 40, pages 51–62. EDP Sciences, 2013.
[25] Fabien Crouzet, Frédéric Daude, Pascal Galon, Philippe Helluy, JeanMarc Hérard, Olivier Hurisse, and Yujie Liu. Approximate solutions of the BaerNunziato model. In ESAIM: Proceedings, volume 40, pages 63–82. EDP Sciences, 2013.
[26] Martina Deininger, Jonathan Jung, Romuald Skoda, Philippe Helluy, and ClausDieter Munz. Evaluation of interface models for 3D1D coupling of compressible euler methods for the application on cavitating flows. In ESAIM: Proceedings, volume 38, pages 298–318. EDP Sciences, 2012.
[27] Thierry Gallouët, Philippe Helluy, JeanMarc Hérard, and Julien Nussbaum. A twofluid model for dense granular flows. In Finite volumes for complex applications V, pages 439–446. ISTE, London, 2008.
[28] Thierry Gallouët, Philippe Helluy, JeanMarc Hérard, and Julien Nussbaum. Hyperbolic relaxation models for granular flows. ESAIM: Mathematical Modelling and Numerical Analysis, 44(2):371–400, 2010.
[29] Frédéric Golay and Philippe Helluy. Numerical schemes for low Mach wave breaking. International Journal of Computational Fluid Dynamics, 21(2):69–86, 2007.
[30] Sebastien Guisset, Michael Gutnic, Philippe Helluy, Michel Massaro, Laurent Navoret, Nhung Pham, and Malcolm Roberts. Lagrangian/eulerian solvers and simulations for Vlasovpoisson. ESAIM: Proceedings and Surveys, 53:120–132, 2016.
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[32] Philippe Helluy and Frédéric Golay. Applications of the finite volumes method for complex flows: From the theory to the practice. Flow, turbulence and combustion, 76(4):315–329, 2006.
[33] Philippe Helluy, Frédéric Golay, JeanPaul Caltagirone, Pierre Lubin, Stephane Vincent, Deborah Drevard, Richard Marcer, Philippe Fraunie, Nicolas Seguin, Stephan Grilli, et al. Numerical simulations of wave breaking. ESAIM: Mathematical Modelling and Numerical Analysis, 39(3):591–607, 2005.
[34] Philippe Helluy, JeanMarc Hérard, and Hélène Mathis. A wellbalanced approximate riemann solver for compressible flows in variable crosssection ducts. Journal of Computational and Applied Mathematics, 236(7):1976–1992, 2012.
[35] Philippe Helluy, JeanMarc Hérard, Hélène Mathis, and Siegfried Müller. A simple parameterfree entropy correction for approximate riemann solvers. Comptes rendus Mécanique, 338(9):493–498, 2010.
[36] Philippe Helluy, Olivier Hurisse, and Erwan Le Coupanec. Verification of a twophase flow code based on an homogeneous model. International Journal on Finite Volumes, 13, https://hal.archives_ouvertes.fr/hal_01396200, 2016.
[37] Philippe Helluy and Jonathan Jung. A wellbalanced scheme for twofluid flows in variable crosssection ducts. In Finite Volumes for Complex Applications VI Problems & Perspectives, pages 561–569. Springer Berlin Heidelberg, 2011.
[38] Philippe Helluy and Jonathan Jung. A coupled wellbalanced and random sampling scheme for computing bubble oscillations. In ESAIM: Proceedings, volume 35, pages 245–250. EDP Sciences, 2012.
[39] Philippe Helluy and Jonathan Jung. OpenCL simulations of twofluid compressible flows with a random choice method. International Journal of Finite Volumes ( https://hal.archives_ouvertes.fr/hal_00759135/), 10, 2013.
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[41] Philippe Helluy, Sylvain Maire, and Patrice Ravel. New higher order numeric quadratures for regular or singular functions on an interval, applications for the helmholtz integral equation. In Second Symposium on Multibody Dynamics and Vibration, september, pages 12–16, 1999.
[42] Philippe Helluy, Sylvain Maire, and Patrick Ravel. High order numerical integration of regular or singular functions on an interval. Comptes Rendus de l’Academie des Sciences Series I Mathematics, 9(327):843–848, 1998.
[43] Philippe Helluy, Hélène Mathis, and Siegfried Müller. An ale averaging approach for the computing of bubble oscillations. Finite Volume for Complex Applications V, ISTE and Wiley, pages 487–494, 2008.
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[45] Philippe Helluy, Laurent Navoret, Nhung Pham, and Anaïs Crestetto. Reduced VlasovMaxwell simulations. Comptes Rendus Mécanique, 342(1011):619–635, 2014.
[46] Philippe Helluy, Nhung Pham, and Anaïs Crestetto. Spaceonly hyperbolic approximation of the Vlasov equation. In ESAIM: Proceedings, volume 43, pages 17–36, 2013.
[47] Philippe Helluy and Nicolas Seguin. Relaxation models of phase transition flows. ESAIM: Mathematical Modelling and Numerical Analysis, 40(2):331–352, 2006.
[48] Philippe Helluy and Thomas Strub. MultiGPU numerical simulation of electromagnetic waves. ESAIM: Proceedings and Surveys, 45:199–208, 2014.
[49] Philippe Helluy, Thomas Strub, Michel Massaro, and Malcolm Roberts. Asynchronous OpenCL/MPI numerical simulations of conservation laws. In Software for Exascale Computing  SPPEXA 20132015, pages 547–565. Springer International Publishing, 2016.
[50] Michel Massaro, Philippe Helluy, and Vincent Loechner. Numerical simulation for the MHD system in 2D using OpenCL. ESAIM: Procs., 45:485–492, 2014.
[51] Siegfried Müller, Mathieu Bachmann, Dennis Kröninger, Thomas Kurz, and Philippe Helluy. Comparison and validation of compressible flow simulations of laserinduced cavitation bubbles. Computers & fluids, 38(9):1850–1862, 2009.
[52] Siegfried Müller, Philippe Helluy, and Josef Ballmann. Numerical simulation of a single bubble by compressible twophase fluids. International Journal for Numerical Methods in Fluids, 62(6):591–631, 2010.
[53] Julien Nussbaum, Philippe Helluy, JeanMarc Herard, and Barbara Baschung. Multidimensional twophase flow modeling applied to interior ballistics. Journal of Applied Mechanics, 78(5):051016, 2011.
[54] Julien Nussbaum, Philippe Helluy, JeanMarc Hérard, and Alain Carriere. Numerical simulations of gasparticle flows with combustion. Flow, turbulence and combustion, 76(4):403–417, 2006.
[55] Nhung Pham, Philippe Helluy, and Anaïs Crestetto. Spaceonly hyperbolic approximation of the Vlasov equation. In ESAIM: Proceedings, volume 43, pages 17–36. EDP Sciences, 2013.
[56] Nhung Pham, Philippe Helluy, and Laurent Navoret. Hyperbolic approximation of the fourier transformed vlasov equation. In ESAIM: Proceedings and Surveys, Congrés SMAI, Seignosse, 2731 mai 2013, volume 45, pages 379–389. EDP Sciences, 2014.
[57] Sandra Rouy and Philippe Helluy. Mathematical and numerical modeling of a twophase flow by a level set method. In Finite volumes for complex applications II, pages 833–840. Hermes Sci. Publ., Paris, 1999.
[58] Lauriane Schneider, Raphaël di Chiara Roupert, Gerhard Schäfer, and Philippe Helluy. Highly gravitydriven flow of a napl in watersaturated porous media using the discontinuous galerkin finiteelement method with a generalised godunov scheme. Computational Geosciences, 19(4):855–876, 2015.
[59] Thomas Strub, Nathanaël Muot, and Philippe Helluy. Méthode galerkin discontinue appliquée à l’électromagnétisme en domaine temporel. In 17e Colloque International et Exposition sur la Compatibilité Electromagnetique https://hal.archives_ouvertes.fr/hal_01108010, 2014.
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[61] Philippe Helluy and Jonathan Jung. Conservative scheme for twofluid compressible flows without pressure oscillations. Oberwolfach Reports, 10(2):1691–1694, 2013.
[62] Philippe Helluy, Michel Massaro, Laurent Navoret, Nhung Pham, and Thomas Strub. Reduced VlasovMaxwell modeling. In PIERS Proceedings, Guangzhou, 2014, pages 2628–2632, 2014.
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[64] Sandra Rouy, Philippe Helluy, and Samuel Kokh. Testcase no 13: Shock tubes (pa). Multiphase Science and Technology, 16(13):87–96, 2004.