6-8 avr. 2016 Lyon (France)
Mathematical modeling and numerical methods for HPC of multi-scale two-phase flow and combustion engineering applications
Marc Massot  1  
1 : Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion  (EM2C)  -  Site web
CNRS : UPR288, Ecole Centrale Paris
Grande voie des vignes 92295 CHATENAY MALABRY CEDEX -  France

The present communication aims at presenting the effort, which has been taking place in the mathematics
team of Laboratory EM2C at former Ecole Centrale Paris, in order to develop new generations of models
and numerical methods for the predictive simulation of multiscale engineering problems. The application
fields are strongly related to the simulation of combustion chambers with liquid fuel injection, which
represent a major challenge for the engineering and industrial communities, but cover also physics of
plasmas, biomedical engineering, etc. The originality of the approach is to tackle the whole range of
disciplines, from mathematical modeling, development of numerical methods and their analysis in sti
multiscale context, to their ecient implementation on parallel architectures in the framework of
HPC and their validation through comparisons with experimental measurements. Once these models and
methods have proved to be scalable and ecient, they can be transferred to semi-industrial and industrial
codes such as AVBP, CEDRE or IFP-C3D. In this presentation, we will mainly focus on mathematical 
modeling and numerical simulation of two major issues in combustion chambers as building blocks 
of a long-term project : the description of the liquid spray as well as the resolution of the dynamics of reaction fronts. 
After briefly introducing the context, we will highlight the strongly multi-scale character of such flows and the various strategies in
terms of both modeling, numerical methods and implementation on parallel architectures with
two types of HPC strategies : either (1) a scalable and efficient distributed-memory algorithm based on
robust and accurate methods or (2) a shared-memory algorithm which makes it possible to perform a 3D
detailed simulation on a standard computer using adaptation in time and space with error control.


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