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Current position

At the Observatoire de Paris.

Activities at the Maison de la simulation

With the development of High Performance Computing infrastructures, we can now have access to supercomputers that makes possible major breakthroughs in various scientific domains. Such achievement requires adapted computational tools to these architectures.

My work was to provide an expertise, in terms of High Performance Computing, to projects that have awarded some hours on the Curie supercomputer through the PRACE program (and eventually the GENCI program).

I participated in these different projects to develop efficient massively parallel algorithms with some specific optimizations to the Curie system architecture. This means generally that each code needs to stay robust, efficient and have a good scalability when we highly increase the number of cores.


AstroParticule et Cosmologie (APC) activities

The observation of the Cosmic Microwave Background (CMB) is one of the most enriching way for the study and the comprehension of the past of our universe. Current and future experiments are more and more sophisticated and need to deal with an increasing amount of numerical data.

My work is to provide adapted numerical tools for the CMB data analysis by using efficient computational algorithms on massively parallel architectures. For this purpose, we develop the Midapack library, distributed under the LGPL license (see download section). For example, this gives all the tools we need to solve a Maximum likelihood mapmaking problem for the CMB with a huge amount of data distributed all over the processors.

In particular, I worked on the algorithms related to the Toeplitz algebra which specific one is the band diagonal and piecewise Toeplitz matrix. This particular matrix can represent, in more physical terms, the noise correlation matrix needed to solve the mapmaking equation. These algorithms exploit the specific structure of such matrices to provide efficient algorithms based mainly on FFTs and Circulant matrices.

The proposed algorithms are stable, robust and have a good scalability on many processors using combined MPI/OMP communications. This gives a large flexibility in the use of these routines and can be easily optimized for a particular computing architecture. You can refer to the library documentation for more details on these routines.

This work has been supported in part by French National Research Agency (ANR) through COSINUS program (project MIDAS no. ANR-09-COSI-009).


Postdoc activities

During my postdoctoral research at the ENS de Cachan, I was working on the compressible multiphase flows modeling. My main work was to continue to develop a "home made" numerical code by including an order 2 FVCF (Finite Volume with Characteristic Fluxes) method using a MUSCL scheme with a least square gradient reconstruction. The code was then tested and validated on classicals test cases, as for example the famous Sod shock tube problem.

I also study this upwind finite volume method for the solution to the compressible Euler equation for low Mach numbers. We used the famous application of the Kelvin-Helmholtz instability, as a simulation of a vortex sheet roll-up, to show the benefits to renormalize the numerical diffusion of the scheme.

This classical hydrodynamical instability occurs when a shear velocity is present. The interface between the two flows with different tangential velocities is unstable and rolls develop. We show that we can capture the shear flows as the local Mach number M (which is the ratio of the norm of velocity in the fluid to the speed of sound) goes to zero.

The final purpose of this kind of work is to build a numerical scheme that behaves well for both compressible and (almost) incompressible flows. This is one of the most challenging problem in CFD. Finite volume methods for compressible flows have been designed in order to capture shocks and to calculate flows dominated by convection. They are therefore challenged when the local Mach number goes to zero.

keywords :
Compressible multiphase flows modeling, Kelvin-Helmholtz Instability, Low Mach Number Flows, Finite Volume Method, Numerical Stability.

Thesis research

Title :
"Méthode de discrétisation pour la modélisation par éléments analytiques en hydrogéologie quantitative. Application aux écoulements en régimes permanents et transitoires" (2006, ENS des Mines de St-Etienne).
Subject :
La méthode des éléments analytiques présente une alternative innovante par rapport aux méthodes numériques classiquement employées pour la modélisation des écoulements souterrains. C’est une méthode basée sur des éléments aux frontières permettant d’exploiter de manière optimale une représentation vectorielle du maillage.
Mon travail de thèse a permis de contribuer à l’amélioration des techniques de modélisation pour cette méthode numérique selon deux aspects majeurs :
– Un aspect assez pratique avec la conception d'outils de discrétisation utilisant des algorithmes de génération de maillage optimisés pour les éléments analytiques ;
– Un aspect plus théorique avec l’établissement d'une méthode numérique permettant d'étendre la méthode des éléments analytiques à des modélisations numériques en régime transitoire.
Ces différents outils ont pu s’insérer dans une démarche de modélisation générale pour un cas d’étude réel. Un modèle conceptuel de la physique de cet aquifère a été construit pour obtenir une représentation indépendante du choix de la discrétisation numérique.
Pour de plus amples informations sur ce travail, vous pouvez lire le résumé de ma thèse en francais (Also available in English version). Vous pouvez aussi télécharger le manuscript de thèse complet.

Selected Publications

F. DAUVERGNE, J.-M. GHIDAGLIA, F. PASCAL, J.-M. ROVARCH, Renormalization of the numerical diffusion for an upwind finite volume method. Application to the simulation of Kelvin-Helmholtz instability, in Finite Volumes for Complex Applications V, Problems and perspectives, R. Eymard and J.-M. Herard eds., Wiley, 2008, pp. 321-328.

F. DAUVERGNE. Méthode de discrétisation pour la modélisation par éléments analytiques en hydrogéologie quantitative. Application aux écoulements en régimes permanents et transitoires. Thèse de doctorat, École Nationale Supérieure des Mines de Saint-Etienne, 2006. (auteur principal)

F. DAUVERGNE, D. MIMOUN, ET D. GRAILLOT. Comparison of the vector and the grid based approaches for the groundwater modeling. Dans International Symposium of the Aquifers Systems Management, Dijon, France, 2006. (auteur principal)

F. DAUVERGNE ET D. GRAILLOT. Discretization Support System for Groundwater Modeling Based on Analytic Elements. Dans 5th International Conference on the Analytic Element Method, Manhattan, Kansas, USA, 2006. (auteur principal)

D. MIMOUN, F. PARAN, F. DAUVERGNE ET D. GRAILLOT. Étude méthodologique du fonctionnement hydrologique et morphologique du fleuve pour la gestion des ressources en eaux superficielles et souterraines de l’Écozone du Forez. Rapport technique, 121p, École Nationale Supérieure des Mines de Saint-Etienne, France, 2006. (Co-auteur)

F. DAUVERGNE, D. MIMOUN, ET D. GRAILLOT. Comparison between FDM and AEM for modeling a local aquifer in France. Dans Fourth International Conference on the Analytic Element Method, Saint Etienne, France, 2003. (auteur principal)