Ecoulements et conditions aux limites particulières appliquées en hydrogéologie et théorie mathématique des processus de dissolution/précipitation en milieux poreux

Abstract : In environmental sciences and more specifically in hydrogeology
phenomenological problems are numerous and lead the scientist in front of the
study of Partial Differential Equations (PDE's) through a large amount of
various different models.

A natural phenomenon may be studied from different angles. It depends on its
main type which could be physical, mechanical, chemical ... Considered
independently and under assumption of sufficient fine scale of observation,
this phenomenon is reasonably well understood and modeled. This is not the
case for multi-physics, coupled physics and chemistry problems, flow problems
closed to interfaces of domains with different structure where the phenomenon
itself is not clearly handled. What 's happening if the same microscopic
behavior is considered at a larger (meso or macroscopic) scale ?

A good understanding of the boundary conditions is required as well as their
modeling which is the "key" in the study of natural phenomenon.

We will see through (un)coupled multi-domain problems with wall laws (Navier,
Beavers and Joseph), chemical processes (Duijn-Knabner's model and the Taylor
dispersion) how it is possible to solve numerically and partially those
difficulties with techniques based on recent mathematical analysis
(homogenization, multi-scale theory, and asymptotic development).

Results of simulations realized with a PDE's solver software called SciFEM
(for Scilab Finite Element Method) made for the needs of this thesis will
emphasize our discussion.
Document type :
Theses
Complete list of metadatas

Cited literature [44 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00132036
Contributor : Vincent Devigne <>
Submitted on : Tuesday, February 20, 2007 - 9:50:16 AM
Last modification on : Friday, October 26, 2018 - 10:30:41 AM
Long-term archiving on : Wednesday, April 7, 2010 - 12:17:20 AM

Identifiers

  • HAL Id : tel-00132036, version 1

Citation

Vincent Devigne. Ecoulements et conditions aux limites particulières appliquées en hydrogéologie et théorie mathématique des processus de dissolution/précipitation en milieux poreux. Mathématiques [math]. Université Claude Bernard - Lyon I, 2006. Français. ⟨tel-00132036⟩

Share

Metrics

Record views

1161

Files downloads

737