Professor, computational engineering.

Philippe Helluy


Born 1 June 1968 in Trier (Germany)
French citizen
Married, three children (22, 19 and 11)

1 Research
2 Inria Tonus team
3 Teaching
4 Software
5 Collective activities
6 Project: the Discontinous Galerkin Lattice Boltzmann Method (DGLBM)
7 Bibliography
Personal address

7 rue des peupliers,
67117 Furdenheim,

Professional address

7 rue Descartes,
67000 Strasbourg,

Research subjects

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 Navier-Stokes and multiphase flows. More recently I have done research on numerical methods for plasma physics: Magneto-Hydro-Dynamics (MHD) and Vlasov-Maxwell models.

Teaching subjects

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 non-closed list of examples of given lectures:






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: Pierre-Alain 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


Full Professor at “Institut de Recherche Mathématique Avancée”, IRMA UMR CNRS 7501. First class since October 2012.

Université de Strasbourg (UDS)

1 Research

1.1 History

After aeronautics engineering studies, I did my PhD under the supervision of Pierre-Alain 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 Navier-Stokes 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.

1.2 Main topics

In this paragraph I present shortly a few of my favorite former works.

1.2.1 Gas-liquid flow modelling

In this work [8] with Thomas Barberon and Sandra Rouy, we studied a compressible gas-liquid flow occurring in a submarine missile ejection device. We applied a fully Eulerian finite volume method able to track naturally the liquid-gas interface. For obtaining correct results it is necessary to adapt carefully several techniques: contact preserving schemes, time-dependent boundary condition that change of type, local time stepping. We were then able to reproduce precisely actual experiments. On Figure 1 the liquid-gas interface can be seen at different times.


Figure 1: Evolution of the liquid (in red) and gas (in purple) in the gas generator at several times.

I used the same kind of approaches for computing wave breaking. See

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 liquid-vapor 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 gas-liquid problems without pressure oscillations at the gas-liquid 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.

1.2.2 Granular flows

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 pg of the gas and the solid pressure ps are linked by a pressure equilibrium relation of the form

p = p + R,
 s   g

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.

1.2.3 Thermodynamics and (max,+) algebra

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

f∗(p) = max(p ⋅x − f(x)).

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

a ⊕ b := max(a,b), a⊙ b := a +b

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)

Ωf(x)dx  ⊕
x∈Ω f(x) = max

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: fˆ (s) = f(x)exp(isx)dx Legendre: f(s) = ⊕
x f(x) χ(s,x) = max
  xsx + f(x)

Convolution: (f g)(x) = yf(x y)g(y)dy Sup-convolutionfg(x) = suypf(x y) + g(y)

(f g) = ˆfĝ (fg) = fg = 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 sup-convolution 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 εi(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 pi(μ,θ) is then the Legendre transform of εi(ρ,σ). After a miscible mixture of the two components, the pressure and energy are given by

p = p1 + p2, ε = ε1□ε2

where denotes the sup-convolution operation. For an immiscible mixture the relations become

p = max(p1,p2),  ε = co min(ε1,ε2),

where co(f) denotes the convex envelope of f.

It is much easier to compute max and + operations than sup-convolutions 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.

1.2.4 GPU and hybrid computing

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 Particle-In-Cell (PIC) method and a Discontinuous Galerkin (DG) method for Vlasov-Maxwell simulations. The method is implemented on GPU with OpenCL. It is applied to the numerical simulation of a medical X-ray generator. With our software, we were awarded a prize at the AMD OpenCL innovation challenge in 2011

With Jonathan Jung I also applied multi-GPU 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 liquid-shock interaction is shown on Figure 2)


pict pict

Figure 2: Liquid droplet (yellow and red) hit by a gas shock wave on 20,000×5,000 mesh. Several zoom levels.

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 home-made 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):

1.2.5 Other works

Navier-Stokes theory In this paper [12] written with F. Golay, we prove a rigorous mathematical result of existence and uniqueness for weakly compressible Navier-Stokes 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 Crouzeix-Raviart 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).


Figure 3: Contracting constant C dependence on the Mach number (K)

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.


Figure 4: Visualization of the amplitude of the initial (top), true (middle) and inverted (bottom) acoustic field. After the assimilation process, the inverted and the true fields are nearly identical. The acoustic source is created by a hydrophone on the left. The measurements are at the right boundary of the computational domain. The unknowns are the variations of the bottom absorption coefficient.

1.3 PhD supervisions

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.






present position



Univ. Toulon/ M.-C. Pélissier

Numerical simulation of compressible flows with phase transition

December 2002

General Manager at TMH Offshore Engineering Kuala Lumpur, Malaysia



UDS, É. Sonnendrücker

Numerical simulation for plasma physics

October 2012

Assistant professor Nantes University



UDS-Région Alsace/L. Navoret

Kinetic methods for acoustics. Application to room acoustic numerical modeling.


Pierre GLANC


UDS, M. Mehrenberger

Semi-Lagrangian numerical methods for plasma physics

January 2014

Postdoc, ENS Lyon



UDS, E. Franck

Lattice-Boltzmann approaches for magnetohydrodynamics


Jonathan JUNG


UDS, J.-M. Hérard

Compressible Multiphase flows, GPU simulations

October 2013

Assistant Professor University of Pau

Yujie LIU


EDF Paris, J.-M. Hérard

Water hammer simulation in nuclear plants pipes.

September 2013

Assistant Professor Sun Yat-sen. School of Data and Computational Science




Automatic compilation. Application to scientific software. Collaboration with computer scientists.

September 2016

Software research engineer, Lyon.




Magnetohydrodynamics, astrophysics. Hybrid CPU/GPU computing. Collaboration with computer scientists and astrophysicists

December 2016

Temporary research engineer, AxesSim.



EDF Paris/J.-M. Hérard

Thermodynamics of multiphase flows. Numerical methods for hyperbolic systems.

September 2010

Assistant professor, University of Nantes



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


UDS, L. Navoret

Reduction methods for Vlasov equation and plasma physics.

December 2016

Temporary assistant professor, Strasbourg

Sandra ROUY


Univ. Toulon/ M.-C. Pélissier

Numerical simulation of compressible air-water flows

December 2000

Associate head of scientific community Sopra (software engineering)



UDS, G. Schäfer

Numerical simulations of geophysical flows

February 2015

Preparation of teacher exams UDS

Thomas STRUB


CIFRE, AxesSim company Illkirch

Numerical simulations for electromagnetism on GPU

March 2015

Permanent research engineer at AxesSim




Optimization of hybrid CPU/GPU simulations for electromagnetism. Interaction with the human body.


1.4 Prize

With Anaïs Crestetto I was awarded the fourth prize at the AMD OpenCL innovation challenge 2011: “Numerical simulation of a medical X-ray generator on GPU:

1.5 Collaborations

Here is a non-exhaustive list of present and former collaborations (the PhD students are listed in the above table).

1.6 Organizations of scientific events

I was co-organizer of several workshops and conferences. For instance:

I am regularly invited to conferences, workshops or summer schools. For instance:

1.7 Reviews

1.7.1 Journals

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:

1.7.2 Other reviews

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.

2 Inria Tonus team

2.1 Presentation

When I arrived in Strasbourg in 2006, Eric Sonnendrücker was head of an Inria project-team CALVI (CALcul scientifique et VIzualization). In 2012 he obtained a position in Garching at the Max-Planck-Institut für Plasmaphysik.

I became head of CALVI. See .

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

As of December 2016, TONUS is composed of the following permanent researchers:

Post-doc researchers: David Coulette, Laura Mendoza.

PhD: Nicolas Bouzat, Ksander Ejjaaouani, Pierre Gerhard, Conrad Hillairet, Michel Massaro, Nhung Pham, Bruno Weber.

2.2 Objectives

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 (temperature150 × 106K). In the long term it might become a way to produce clean energy.

The plasma is confined with strong magnetic fields in a doughnut-shaped 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 time-dependent in a six-dimensional phase space. The Vlasov equation reads

∂tf + v⋅∇xf + (− ∇ Φ +v × B)⋅∇vf = C(f),

where B is the given magnetic field imposed by the tokamak superconducting coils, Φ is the electric potential, solution of the Poisson equation


− Δ Φ = ρ, ρ(x,t) = vf (x,v,t)dv,

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 high-dimensional phase space, it is also a challenge for HPC. It requires the full power of the biggest supercomputers for obtaining realistic simulations.

2.3 Achievements

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 semi-Lagrangian methods for solving kinetic equations. The methods are implemented in the Selalib library, which is a joint software project between Inria and the Max-Planck-Institut für Plasmaphysik in Garching. The most efficient semi-Lagrangian 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

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:

3 Teaching

3.1 Given lectures

Since my PhD I teach in various fields of physics, mathematics and computer science to future engineers or mathematicians. Here is a non-closed list of examples:

Here are some links (generally in French, but in English sometimes) with teaching material for students:

3.2 Examples

In this section I give two examples of teaching sessions at the master level.

3.2.1 Master lecture (first year)

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

∂t  2
∂x2 = 0,
u(x,0) = u0(x),
∂x(0,t) = ∂u-
∂x(L,t) = 0.
The initial condition has the following shape
        {1  if x ∈ [L, 3L],
u0(x) =           4  4
         0  otherwise.

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:

3.2.2 Master lecture (second year)

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 Tu(x) is a solution of the stationary heat equation

− ΔTu = 0.

On a part of the room boundary Γd there is a (badly insulated) window where we apply Dirichlet condition

Tu = 0 on Γ d.

On the rest of the boundary Γn we apply the control (a heat flux)

-∂n-= u.

We want the temperature to be close to a constant desired temperature

Tu ≃ Θ

(for instance Θ = 20°C). We thus consider the cost function

      1 ∫            ϵ∫
J(u) =-   |Tu − Θ |2 +-    u2.
      2  Ω           2 Γ n

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 ( This software allows to implement in a very easy way various finite element variational methods.

Other optimal control studies (in French) are proposed here:

4 Software

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 gas-water inside a submarine gas generator. The flow is solved by the finite volume method in axisymmetric geometry with special tricks for handling liquid-gas interface, boundary conditions and local time-stepping (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 time-stepping.

EOLENS is a modification of CM2 which contains additional k ϵ turbulence models. It was sold in 2006 to the PRINCIPIA company.

4.3 DIWA

DIWA it is a research software for solving Vlasov-Maxwell equations by a Particle-In-Cell (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 X-ray 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 X-rays. 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:

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 gas-liquid compressible flows. A video demonstrating a shock-bubble interaction can be seen at:

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 multi-GPU 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 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 Non-linéaire Appliqué aux PlaSmas”) is a research software project developed in my team for handling this kind of hybrid computing approach. 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:

5 Collective activities

5.1 Official responsibilities

In my career I participated to the collective life of my universities. Here is also a non-closed list of examples:

5.2 Fundings

Here is a list of some supports that I obtained for my research projects.

5.3 Contracts

In my career I had several occasions to realize applied research contracts with industry or less academic institutions:

5.3.1 Banyuls

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):

5.3.2 DCN Toulon

In 1997-2000 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.

5.3.3 Principia

in 2006 I made a software study of 30kfor 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.

5.3.4 AxesSim

AxesSim is a software company in Strasbourg, specialized in electromagnetic simulations.

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 kfor 6 years). This collaboration is also supported by DGA (French defense agency) and BPI (French public bank for investment).

6 Project: the Discontinous Galerkin Lattice Boltzmann Method (DGLBM)

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.

6.1 Kinetic modeling

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:

When the relaxation time τ is small, the kinetic equation provides an approximation of the hyperbolic conservative system

∂tw + ∇ ⋅F(w) = 0,


Fi(w) =   viMw  (v)K (v)dv.

The main idea is that numerical solvers for the linear scalar transport equation lead to natural solvers for the non-linear 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:

6.2 DGLBM: future works

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:

7 Bibliography

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:

See also my Google Scholar page:

7.1 Thesis, preprints, unpublished works

[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.

[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 Banyuls-sur-mer, 1998.

[3]   Philippe Helluy. Simulation numérique des écoulements multiphasiques: de la théorie aux applications.". Habilitation thesis, Université de Toulon, 2005.

[4]   Philippe Helluy. A portable implementation of the radix sort algorithm in OpenCL., 2011.

[5]   Christophe Steiner, Michel Mehrenberger, Nicolas Crouseilles, and Philippe Helluy. Quasi-neutrality equation in a polar mesh., 2015.

[6]   Philippe Helluy. Stability analysis of an implicit lattice boltzmann scheme., 2016.

[7]   David Coulette, Emmanuel Franck, Philippe Helluy, Michel Mehrenberger, and Laurent Navoret Palindromic discontinuous Galerkin method for kinetic equations with stiff relaxation., 2016.

7.2 Selected works

[8]   Thomas Barberon, Philippe Helluy, and Sandra Rouy. Practical computation of axisymmetrical multifluid flows. International Journal on Finite Volumes, 1:1–34, 2003.

[9]   Thomas Barberon and Philippe Helluy. Finite volume simulation of cavitating flows. Computers & fluids, 34(7):832–858, 2005.

[10]   Philippe Helluy and Jonathan Jung. Interpolated pressure laws in two-fluid simulations and hyperbolicity. In Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, pages 37–53. Springer International Publishing, 2014.

[11]   Philippe Helluy and Hélène Mathis. Pressure laws and fast legendre transform. Mathematical Models and Methods in Applied Sciences, 21(04):745–775, 2011.

[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, 1998.

[13]   Jean-Claude Le Gac, Yann Stephan, Mark Asch, Philippe Helluy, and Jean-Pierre 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.\~helluy/ADMIN/CV/acoustic2.pdf

7.3 Publications

In the following list I only give papers with sufficient materials (typically more than 5 pages) that have been published after a review process in a journal or in conference proceedings

[14]   Christoph Altmann, Thomas Belat, Michael Gutnic, Philippe Helluy, Helene Mathis, Eric Sonnendruecker, Wilfredo Angulo, and Jean-Marc Herard. A local time-stepping discontinuous galerkin algorithm for the MHD system. In ESAIM: proceedings, volume 28, pages 33–54. EDP Sciences, 2009.

[15]   Mark Asch, Jean-Claude Le Gac, and Philippe Helluy. An adjoint method for geoacoustic inversions. In PICOF’02: problèmes inverses, contrôle et optimisation de formes.\~helluy/ADMIN/CV/acoustic.pdf, pages 23–29, 2002.

[16]   Mathieu Bachmann, Philippe Helluy, Jonathan Jung, Hélene Mathis, and Siegfried Müller. Random sampling remap for compressible two-phase flows. Computers & Fluids, 86:275–283, 2013.

[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, Pierre-Alain Mazet, and Philippe Helluy. Resolution of the non-stationary 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, Jean-Marc 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. Second-order 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 physics-based preconditioning with high-order galerkin discretization for hyperbolic wave problems., 2016.

[22]   Anaïs Crestetto and Philippe Helluy. Multi-water-bag 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 Vlasov-Maxwell 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, Jean-Marc Hérard, Olivier Hurisse, and Yujie Liu. Approximate solutions of the Baer-Nunziato model. In ESAIM: Proceedings, volume 40, pages 63–82. EDP Sciences, 2013.

[26]   Martina Deininger, Jonathan Jung, Romuald Skoda, Philippe Helluy, and Claus-Dieter Munz. Evaluation of interface models for 3D-1D 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, Jean-Marc Hérard, and Julien Nussbaum. A two-fluid model for dense granular flows. In Finite volumes for complex applications V, pages 439–446. ISTE, London, 2008.

[28]   Thierry Gallouët, Philippe Helluy, Jean-Marc 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 Vlasov-poisson. ESAIM: Proceedings and Surveys, 53:120–132, 2016.

[31]   Philippe Helluy and Sandrine Dayma. Convergence d’une approximation discontinue des systemes du premier ordre. CR Acad. Sci. Paris Sér. I Math, 319(12):1331–1335, 1994.

[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, Jean-Paul 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, Jean-Marc Hérard, and Hélène Mathis. A well-balanced approximate riemann solver for compressible flows in variable cross-section ducts. Journal of Computational and Applied Mathematics, 236(7):1976–1992, 2012.

[35]   Philippe Helluy, Jean-Marc Hérard, Hélène Mathis, and Siegfried Müller. A simple parameter-free 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 two-phase flow code based on an homogeneous model. International Journal on Finite Volumes, 13,, 2016.

[37]   Philippe Helluy and Jonathan Jung. A well-balanced scheme for two-fluid flows in variable cross-section 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 well-balanced 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 two-fluid compressible flows with a random choice method. International Journal of Finite Volumes (, 10, 2013.

[40]   Philippe Helluy and Jonathan Jung. Two-fluid compressible simulations on GPU cluster. ESAIM: Proceedings and Surveys, 45:349–358, 2014.

[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.

[44]   Philippe Helluy, Pierre-Alain Mazet, and Patricia Klotz. Approximation of the unstationary Maxwell equations in an unbounded domain asymptotic behaviour. Recherche Aerospatiale/Aerospace Research (ISSN 0034-1223), no. 5, p. 365-377, 5:365–377, 1994.

[45]   Philippe Helluy, Laurent Navoret, Nhung Pham, and Anaïs Crestetto. Reduced Vlasov-Maxwell simulations. Comptes Rendus Mécanique, 342(10-11):619–635, 2014.

[46]   Philippe Helluy, Nhung Pham, and Anaïs Crestetto. Space-only 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. Multi-GPU 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 2013-2015, 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 laser-induced 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 two-phase fluids. International Journal for Numerical Methods in Fluids, 62(6):591–631, 2010.

[53]   Julien Nussbaum, Philippe Helluy, Jean-Marc Herard, and Barbara Baschung. Multi-dimensional two-phase flow modeling applied to interior ballistics. Journal of Applied Mechanics, 78(5):051016, 2011.

[54]   Julien Nussbaum, Philippe Helluy, Jean-Marc Hérard, and Alain Carriere. Numerical simulations of gas-particle flows with combustion. Flow, turbulence and combustion, 76(4):403–417, 2006.

[55]   Nhung Pham, Philippe Helluy, and Anaïs Crestetto. Space-only 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, 27-31 mai 2013, volume 45, pages 379–389. EDP Sciences, 2014.

[57]   Sandra Rouy and Philippe Helluy. Mathematical and numerical modeling of a two-phase 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 gravity-driven flow of a napl in water-saturated porous media using the discontinuous galerkin finite-element 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, 2014.

7.4 Others

[60]   Mathieu Bachmann, Siegfried Müller, Philippe Helluy, and Hélene Mathis. A simple model for cavitation with non-condensable gases. Hyperbolic Problems: Theory, Numerics and Applications (In 2 Volumes), 18:289, 2013.

[61]   Philippe Helluy and Jonathan Jung. Conservative scheme for two-fluid 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 Vlasov-Maxwell modeling. In PIERS Proceedings, Guangzhou, 2014, pages 2628–2632, 2014.

[63]   Julien Nussbaum, Philippe Helluy, Jean-Marc Hérard, and Alain Carrière. Numerical simulations of reactive diphasic gas-particle flows. In 39th AIAA Thermophysics Conference, page 4161, 2007.

[64]   Sandra Rouy, Philippe Helluy, and Samuel Kokh. Test-case no 13: Shock tubes (pa). Multiphase Science and Technology, 16(1-3):87–96, 2004.