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Analyse asymptotique de schémas de résolution de l'équation du transport en régime diffusif

Abstract : The Symbolic Implicit Monte Carlo method (SIMC) gives an approximation of the transport equation. In the original method, this function was supposed constant on each cell of the mesh. We have demonstrated that by taking piecewise linear function, this method becomes asymptotically preserving unlike the constant SIMC method. It means that in a diffusive medium where the collisions are predominant, it gives a correct solution even if the mesh size is large in regard of the mean free path but small enough to solve the diffusion scale. Boundary layers arise in diffusive medium when the incident intensity is anisotropic. We demonstrate and verify numerically that the results of the linear SIMC method can be quite good even if the boundary layers are not meshed at the mean free path scale. We study also linear discontinuous finite elements schemes and demonstrate that these schemes verify the saure asymptotic limit and possess the saure boundary conditions in diffusive medium as the SIMC method.
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https://tel.archives-ouvertes.fr/tel-00363723
Contributor : Ens Cachan Bibliothèque <>
Submitted on : Tuesday, February 24, 2009 - 12:07:02 PM
Last modification on : Thursday, January 28, 2021 - 3:01:31 PM
Long-term archiving on: : Tuesday, June 8, 2010 - 10:52:02 PM

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  • HAL Id : tel-00363723, version 1

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Gérald Samba. Analyse asymptotique de schémas de résolution de l'équation du transport en régime diffusif. Mathématiques [math]. École normale supérieure de Cachan - ENS Cachan, 2008. Français. ⟨tel-00363723⟩

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