Leak identification in porous media by solving the Cauchy problem

Xavier Escriva; Thouraya N. Baranger; Nejla Hariga Tlatli

doi:10.1016/j.crme.2007.04.001

Leak identification in porous media by solving the Cauchy problem

Presented by: Huy Duong Bui

Xavier Escriva ^1,²; Thouraya N. Baranger ^2,^3,⁴ ; Nejla Hariga Tlatli ⁵

¹ LMFA, CNRS UMR 5509, université de Lyon, 69003 Lyon, France
² Université Lyon-1, 69622 Villeurbanne, France
³ LaMCoS, INSA-Lyon, CNRS UMR5259, 69621 Lyon, France
⁴ Université de Lyon, 69003 Lyon, France
⁵ LAMSIN-ENIT, INAT, Tunisia

Comptes Rendus. Mécanique, Volume 335 (2007) no. 7, pp. 401-406.

Abstract
Résumé

We propose in this Note a method of identifying leak zones in a saturated and homogeneous porous domain by solving a Cauchy problem. The method is based on the minimisation of an energy-like error functional procedure developed in 2006 by Andrieux and Baranger.

Nous proposons dans ce travail, l'identification de fuites dans un domaine poreux homogène et saturé, en résolvant un problème de Cauchy. Cette résolution est effectuée au moyen d'une procédure de minimisation d'une fonctionnelle d'erreur énergétique développée en 2006 par Andrieux et Baranger.

Received: 2007-04-06
Accepted: 2007-04-17
Published online: 2007-06-05

DOI: 10.1016/j.crme.2007.04.001

Keywords: Porous media, Leak identification, Data completion, Cauchy problem, Darcy law
Mots-clés : Milieux poreux, Identification de fuites, Complétion de données, Problème de Cauchy, Loi de Darcy

Author's affiliations:

Xavier Escriva ^{1, 2}; Thouraya N. Baranger ^{2, 3, 4}; Nejla Hariga Tlatli ⁵

¹ LMFA, CNRS UMR 5509, université de Lyon, 69003 Lyon, France
² Université Lyon-1, 69622 Villeurbanne, France
³ LaMCoS, INSA-Lyon, CNRS UMR5259, 69621 Lyon, France
⁴ Université de Lyon, 69003 Lyon, France
⁵ LAMSIN-ENIT, INAT, Tunisia

@article{CRMECA_2007__335_7_401_0,
     author = {Xavier Escriva and Thouraya N. Baranger and Nejla Hariga Tlatli},
     title = {Leak identification in porous media by solving the {Cauchy} problem},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {401--406},
     publisher = {Elsevier},
     volume = {335},
     number = {7},
     year = {2007},
     doi = {10.1016/j.crme.2007.04.001},
     language = {en},
}

TY  - JOUR
AU  - Xavier Escriva
AU  - Thouraya N. Baranger
AU  - Nejla Hariga Tlatli
TI  - Leak identification in porous media by solving the Cauchy problem
JO  - Comptes Rendus. Mécanique
PY  - 2007
SP  - 401
EP  - 406
VL  - 335
IS  - 7
PB  - Elsevier
DO  - 10.1016/j.crme.2007.04.001
LA  - en
ID  - CRMECA_2007__335_7_401_0
ER  -

%0 Journal Article
%A Xavier Escriva
%A Thouraya N. Baranger
%A Nejla Hariga Tlatli
%T Leak identification in porous media by solving the Cauchy problem
%J Comptes Rendus. Mécanique
%D 2007
%P 401-406
%V 335
%N 7
%I Elsevier
%R 10.1016/j.crme.2007.04.001
%G en
%F CRMECA_2007__335_7_401_0

Xavier Escriva; Thouraya N. Baranger; Nejla Hariga Tlatli. Leak identification in porous media by solving the Cauchy problem. Comptes Rendus. Mécanique, Volume 335 (2007) no. 7, pp. 401-406. doi : 10.1016/j.crme.2007.04.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.04.001/

References
Cited by

[1] Z. Belhachmi; A. Karageorghis; K. Taous Identification and reconstruction of a small leak zone in a pipe by a spectral element method, J. Sci. Comput., Volume 27 (2006) no. 1–3

[2] F. Santosa; M. Vogelius A computational algorithm for determining cracks from electrostatic boundary measurements, Int. J. Eng. Sci., Volume 29 (1991), pp. 917-938

[3] R. Kohn; M. Vogelius Relaxation of a variational method for impedance computed tomography, Comm. Pure Appl. Math., Volume 40 (1987)

[4] S. Andrieux; T.N. Baranger Solving Cauchy problems by minimizing an energy-like functional, Inv. Prob., Volume 22 (2006), pp. 115-133

[5] T.N. Baranger, S. Andrieux, An optimization approach for the Cauchy problem in linear elasticity, Structural and Multidisciplinary Optimization, , May 2007 | DOI

[6] J. Hadamard Lectures on Cauchy's Problem in Linear Partial Differential Equation, Dover, New York, 1923

Cited by Sources:

Comments - Policy