Rechercher

sur ce site


Accueil du site > Résumés des séminaires > Labo > Adaptive time-space algorithms with error control for the simulations of multi-scale reaction waves : application to plasma physics and combustion simulations

Adaptive time-space algorithms with error control for the simulations of multi-scale reaction waves : application to plasma physics and combustion simulations

Numerical simulations of multi-scale phenomena are commonly used for modeling purposes in many applications such as combustion or plasmas physics. These models raise several difficulties created by the high number of unknowns, the wide range of temporal scales due to detailed chemical kinetic mechanisms, as well as steep spatial gradients associated with very localized fronts of high chemical activity. Furthermore, a natural stumbling block to perform 3D simulations with all scales resolution is either the unreasonably small time step due to stability requirements or the unreasonable memory requirements for implicit methods. In this work, we introduce a new resolution strategy for multi-scale reaction waves based mainly on time operator splitting and space adaptive multiresolution. It considers high order time integration methods for reaction, diffusion and convection problems, in order to build a time operator splitting scheme that exploits efficiently the special features of each problem. Based on theoretical studies of numerical analysis, such a strategy leads to a splitting time step which is not restricted neither by fast scales in the source term nor by restrictive stability limits of diffusive or convective steps, but only by the physics of the phenomenon. Moreover, this splitting time step is dynamically adapted taking into account a posteriori error estimates, carefully computed by a second embedded and economic splitting method. The main goal is then to perform computationally efficient as well as accurate in time and space simulations of the complete dynamics of multi-scale phenomena, considering large simulation domains with conventional computing resources and splitting time steps dictated by the physics of the phenomenon and not by stability constraints associated with mesh size or source time scales. Applications will be presented in the fields of combustion waves and plasma discharges dynamics.

CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46