logo de l'IRMA logo UDS logo INRIA logo CNRS ← Back

Philippe Helluy

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 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 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∈Ωf(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) = ⊕
xf(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 https://community.topcoder.com/amdapp/

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: http://www.i2m.univ-amu.fr/IJFV/

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.