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UID:5845@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20221205T000000
DTEND;TZID=Europe/Paris:20221209T000000
DTSTAMP:20241120T200232Z
URL:https://www.i2m.univ-amu.fr/evenements/discrete-fracture-networks-morl
 et-chair-martin-gander/
SUMMARY:Pairs (CIRM\, Luminy\, Marseille): Discrete Fracture Networks (Morl
 et Chair - Martin Gander)
DESCRIPTION:Pairs: \n\n\n\n\n\n\n\nCIRM - Jean-Morlet Chair \n Martin GANDE
 R &amp\; Florence HUBERT\n\nNumerical Methods for PDEs: Discretization\, I
 terative Solution and Parallelization\n\nMéthodes numériques pour les ED
 P: discrétisation\, solution itérative et parallélisation\n\n\n 2022 - 
 semester 2\n\n\n\n\n\n\n\n\n\n\nRESEARCH IN PAIRS\n​Discrete Fracture Ne
 tworks\n​Date: 5-9 décembre 2022\n\n\n\n\n\n\n\n\n\n\n INVITATION / VIS
 A LETTER \n\n\n\n\n\n PRACTICAL INFO \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\
 n\n\n\n\nDESCRIPTION\nDiscrete fracture networks are models to simulate fl
 ow behavior in the underground in the presence of fractures. In the fractu
 res\, the flow behavior is very different from the flow in the so-called s
 urrounding matrix. The simulation of one fracture thus requires both a dif
 ferent flow model in the fracture from the flow model in the matrix\, and 
 coupling conditions between the thin fracture and the matrix. In addition\
 , the mesh\, in general\, needs to be extremely fine in the fracture compa
 red to the matrix. While this is possible for the simulation of one (or a 
 few fractures)\, it becomes prohibitive when many fractures are present. I
 n the limit of a very large number\, one could then use homogenization tec
 hniques\, but we are interested here in the intermediate\, hard regime\, w
 here the fractures still need to be modeled individually\, and there are m
 any of them. A common method to establish such models consists in integrat
 ing the fracture equations over the fracture width and using some ad hoc a
 pproximations for the coupling conditions [2\, 5\, 1\, 4]. We are interest
 ed here in a systematic construction of reduced order elliptic PDE models 
 for such fractured domains. In [3]\, we derived coupling conditions betwee
 n matrix subdomains\, when the fracture is represented as a hypersurface e
 mbedded in the surrounded rock matrix. These coupling conditions were obta
 ined by analytically eliminating the fracture and encoding the information
  of the fracture in the coupling conditions via a continuous variant of a 
 Schur complement. We then derived local approximations of these coupling c
 onditions using asymptotic expansions when 1 the fracture width goes to ze
 ro. A complete analysis of this approach can be found in [3]. In the prese
 nt project\, we are interested in a different asymptotic regime\, namely a
  fixed small fracture width\, but when the mesh size of the numerical appr
 oximation is going to zero. The advantage of this second approach is that 
 it will be suitable also for fractures with a more realistic fracture widt
 h\, and at the same time optimized for the numerical method used. We will 
 follow in our approach the analogy we know from domain decomposition metho
 ds\, in particular optimized Schwarz methods\, where for transport dominat
 ed flows\, optimized transmission conditions were derived both for the phy
 sical parameter represented by the Peclet number becoming large\, or the n
 umerical mesh parameter becoming small.\n\n\n \n\nPARTICIPANTS\n\n\n 	Mar
 tin Gander (Université de Genève &amp\; Aix-Marseille Université)​\n 
 	Julian Hennicker (Université de Genève)\n 	Roland Masson (Université C
 ôte d'Azur)\n 	Tommaso Vanzan (EPFL Lausanne)\n\n\n\nREFERENCES\n\n\n[1] 
 P. Angot\, F. Boyer\, and F. Hubert. Asymptotic and numerical modelling of
  flows in fractured porous media. ESAIM: Mathematical Modelling and Numeri
 cal Analysis-Modélisation Mathématique et Analyse Numérique\, 43 (2):23
 9–275\, 2009.\n\n[2] E. Flauraud\, F. Nataf\, I. Faille\, and R. Masson.
  Domain decomposition for an asymptotic geological fault modeling. Comptes
  Rendus Mécanique\, 331(12):849–855\, 2003.\n\n[3] M. J. Gander\, J. He
 nnicker\, and R. Masson. Asymptotic analysis for the coupling between subd
 omains in discrete fracture matrix models. In Domain Decomposition Methods
  in Science and Engineering XXV\, LNCSE. Springer Verlag\, 2020. [\n\n4] M
 . Lesinigo\, C. D’Angelo\, and A. Quarteroni. A multiscale darcy–brink
 man model for fluid flow in fractured porous media. Numerische Mathematik\
 , 117(4):717–752\, 2011.\n\n[5] V. Martin\, J. Jaffré\, and J. E. Rober
 ts. Modeling fractures and barriers as interfaces for flow in porous medi
 a. SIAM Journal on Scientific Computing\, ​26(5):1667–1691\, 2005.\n\
 n\n\n\n\n\n\n\nSPONSOR\n\n\n\n\n\n\n\n\n\n\n  \n\n\n\n\n\n\n\n  \n\n\n\n\n
 \n\n\n  \n\n\n\n\n\n\n\n  \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
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 022/03/Morlet-2022-pairs-discrete_fracture_matrix_model-Gander-Hennicker-M
 asson.jpg
CATEGORIES:Manifestation scientifique,Morlet Research in Pairs
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