HYperbolic and Kinetic Equations :
Asymptotics, Numerics, Analysis
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Short presentation of the team F3

Sites of F3 OCC: Nice + Marseille, Toulouse
Team Organizer Y. Brenier

The OCC team has a broad expertise covering most of the assigned tasks. OCC is strongly involved in the study of hyperbolic conservation laws and their numerical simulation, with a large input from kinetic theory. Kinetic schemes, relaxation methods, moment equations, finite volume methods for conservation laws are very active fields, in particular in the Bordeaux and Marseille research groups (tasks 1 , 15 , 16 , involving collaboration with teams I1, I2, D2, D1). The OCC team, mostly through its Nice and Toulouse branches, has also a considerable research activity and training ability in the field of kinetic equations related to transport of charge particles, in particular for plasmas and semi-conductors. Both analytical and numerical aspects at classical and quantum levels, with or without collisions, in homogeneous, periodic or random media are treated (tasks 2 , 6 , 7 , 9 , involving collaborations with A1, D1, D2, E2, F2, S1). An important research effort has been successfully dedicated on one part to the derivation of macroscopic and mesoscopic models (like hyperbolic conservation and diffusion equations and recently turbulence models) thanks to an asymptotic procedure starting from the microscopic level (kinetic or quantum), and on the other part to the construction, the analysis and numerical simulation of novel hybrid models for plasmas and nanostructures coupling kinetic and macroscopic descriptions or quantum and classical descriptions (tasks 3 , 6 , 8 , 16 , involving collaborations with A1, D1, D2, E2, F1, F2, I1, I3). There is also a strong expertise on more specific topics such as shock waves, boundary layer analysis, geometrical optics, classical fields equations, phase transitions (tasks 5 , 11 , 12 , 13 , involving collaborations with D2, F2, G, I1, I2). Industrial applications are at the heart of many researches, with extended collaborations with french atomic energy commission (CEA), aeronautics and space research office (ONERA) and companies (EADS, Dassault, SNPE), french and european space agencies (CNES, ESA). The Toulouse and Nice branches are in the process of being recognized as conventioned teams of the CEA, which already is the case of the Bordeaux branch. Typical problems are radiative transfer, propergol engines, ionic propellers for satellites, electric arc discharges in satellite solar cells, single electron nanoscale memories, etc...

The key scientific staff consists of the following members

- Y. Brenier (TO, HTC) (Nice, 30%)  - S. Lohrengel (Nice, 20%)  - F. Poupaud (SAB) (Nice, 25%),  - M. Rascle (Nice, 25%)  - O. Gues (Marseille, 20%)),     - R. Herbin (Marseille, 20%),  - F. Hubert (Marseille, 20%)  - A. Nouri (TC) (Marseille, 25%),  - T. Gallouet (Marseille, 20%)  - N. Ben Abdallah (Toulouse, 25%),  - P. Degond (SC) (Toulouse, 25%)  - J.-M. Roquejoffre (Toulouse, 25%),  - M.-H. Vignal (Toulouse, 20%)  - J.-P. Vila (Toulouse, 20%),  - R. Abgrall (Bordeaux, 20%)  - D. Aregba (Bordeaux, 30%),  - A. Bachelot (Bordeaux, 20%)  - P. Charrier (Bordeaux, 20%),  - B. Hanouzet (Bordeaux, 30%)  - G. Metivier (Bordeaux, 40%);  

A list of significant publications for the IHP project is as follows :

[1] D. Aregba-Driollet (F3), R. Natalini (I1), Discrete kinetic schemes for multidimensionnal systems of conservation laws , SIAM J. Num. Anal. 37 (2000), 1973-2004.

[2] L. Arkeryd (S1), A. Nouri (F3), On the Milne problem and the hydrodynamic limit for a steady Boltzmann equation model , J. Statist. Phys. 99 (2000), 993-1019.

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