Ezziani, Abdelaâziz (2005) Mathematical and numerical modeling of wave propagation in viscoelastic and poroelastic Media Thesis, ENSTA.

[img]PDF (Annexes)
Restricted to Repository staff only

[img]PDF (Thèse)
Restricted to Repository staff only


Official URL: http://tel.archives-ouvertes.fr/tel-00009179


We are interested in the mathematical and numerical modeling of wave propagation in underground media. We present two propagation model: (i) a generalization of Zener's model for viscoelastic media, (ii) Biot's model for poroelastic media. For each model we achieve a mathematical analysis, In particular, an existence and uniqueness of solution and an energy decay result. For the numerical resolution we construct a method specific to each model, based on a variational approach, a mixed finite elements approximation in space and a finite difference in time. We prove for each scheme obtained, a result of discrete energy decay which provides a sufficient stability condition. To simulate the waves propagation in unbounded domains, we adapt the perfectly matched layers techniques to viscoelastic and poroelastic waves. Finally, we present various numerical validations of the developed methods.

Item Type:Thesis (Thesis)
Uncontrolled Keywords:Energy
Subjects:Mathematics and Applications
ID Code:2508
Deposited By:Julien Karachehayas
Deposited On:07 juin 2007 02:20
Dernière modification:05 juin 2013 09:14

Repository Staff Only: item control page