Modeling and Information Processing

Mathematical Modeling and Numerical Simulation

Mathematical modeling of multi-scale physical systems.

In several physical systems, the problem of scale hampers making predictions using numerical simulation. In fact, in order to describe the evolution of a system, it is often necessary to describe the basic actions that govern its behavior in detail, as these actions generally involve characteristic time or lengths lower by several orders than the characteristic time and lengths of the global system.

Explicit inclusion of these characteristic short times invariably leads to very high computing times, thus making simulation for industry's purpose useless. The modeling work undertaken by the M2SN team aims to offer alternatives, both for physical methods (asymptotic studies, fluid methods, etc) and for numerical methods (implicit process, no local time, etc.), so that these simulations can be used by the industry.

Participants in the M2SN unit: G. Dufour, F. Rogier
Doctorand: P. Seimandi

The fields of application under study are:

• Creation of atmospheric plasma by corona discharge
   
  The study of atmospheric plasma involves several fields of application, whether pertaining to the field of combustion (participation in INCA program), aerodynamics where the aim is on to reduce the aircraft's drag by creating an ionic wind (in the framework of participation in PUMA PRF), or in the field of electromagnetism (modifying an aircraft's radar signature).  The work carried out mainly concerns modeling the "corona" type discharge between two electrodes, in order to simulate the creation of plasma under atmospheric pressure. Then, the aim is to assess the effects of this plasma on the environment, by, for example, estimating the ionic wind created by the discharge.

• Analyzing a satellite's charge, spatial plasmas
   
  This study is part of collaborative effort with the DESP department for development of the free SPIS (Spacecraft Plasma Interaction System) platform to be used for calculating the charge of a satellite surrounded by spatial plasma. The M2SN unit helps by providing fast and adapted numerical methods that are used for calculating electric field, change in densities of species loaded in the plasma and change in the charge of the satellite by defining an equivalent circuit.

• Modeling of two-phase flows with dispersed inclusions
   
  Simulation of mists of droplets is at the heart of evolution of reactive two-phase flows. As part of MOGADIR PRF, we are studying the possibility of modeling the dispersed part, thus basically discreet, using fluid methods. The challenge associated with this modeling is integrating the influence of drop size on the flow and especially giving a method that can calculate the change in the size of drops. Therefore, we propose integrating the CEDRE calculation code of a Multi-Fluids type method within the SPIREE module that is suited to this problem.

• Modeling fluids in complex network
   
  Today, numerical simulation of changes to network (roadways, computing, etc.) is fast restricted by their complexity. The quantity of interactions to be included excludes any intention of exhaustive direct simulation. Therefore, a solution is to model the network's discreet parameters using continuous phenomenon, leading to less costly resolution with regards computing time of equations with partial derivatives. In collaboration with the ISC unit of the DTIM, we are studying this promising avenue for validating and evaluating new AFDX type avionic networks. If we were able to perform calculations on these networks in short time we would eventually be able to develop more efficient and less costly networks.

• Integration of the stochastic aspect into modeling
   
  Taking random phenomena into account is fast growing subject within the numerical community. In fact, numerical simulations are generally based on deterministic methods and a random component is introduced through a lottery before simulation. This therefore requires as many simulations as there are lotteries. As part of ARF STOK, we study different methods of avoiding this, by using stochastic calculations (resolution of EDS and EDPS) and adapted numerical methods (stochastically finite elements, etc.), which can be used to calculate the expectations directly without having recourse to Monte-Carlo type methods.

Last Update: 25 February 2008 - © ONERA 2009 - Terms of use