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<datestamp>2018-01-11</datestamp>
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<publisher>HAL CCSD</publisher>
<title lang=en>Algorithms for coupled mechanical deformations and fluid flow in a porous medium with different time scales</title>
<creator>Daïm, Fatima-Zahra</creator>
<creator>Hilhorst, Danielle</creator>
<creator>Laminie, Jacques</creator>
<creator>Eymard, Robert</creator>
<contributor>Laboratoire de Mathématiques d'Orsay (LM-Orsay) ; Université Paris-Sud - Paris 11 (UP11) - Centre National de la Recherche Scientifique (CNRS)</contributor>
<contributor>Laboratoire de Mathématiques Informatique et Applications (LAMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<contributor>Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA) ; Université Paris-Est Marne-la-Vallée (UPEM) - Fédération de Recherche Bézout - Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12) - Centre National de la Recherche Scientifique (CNRS)</contributor>
<description>International audience</description>
<source>ISSN: 1705-5105</source>
<source>International Journal of Numerical Analysis and Modeling</source>
<publisher>Institute for Scientific Computing and Information</publisher>
<identifier>hal-01449039</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-01449039</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-01449039/document</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-01449039/file/DHLE.pdf</identifier>
<source>https://hal.archives-ouvertes.fr/hal-01449039</source>
<source>International Journal of Numerical Analysis and Modeling, Institute for Scientific Computing and Information, 2009, 5 (4), pp.635-658. 〈http://www.math.ualberta.ca/ijnam/Volume5.htm〉</source>
<source>http://www.math.ualberta.ca/ijnam/Volume5.htm</source>
<language>en</language>
<subject lang=en> Multiscale algorithm</subject>
<subject lang=en> Mixed formulation</subject>
<subject lang=en> Inf-Sup condition</subject>
<subject lang=en>Porous media</subject>
<subject lang=en> Darcy flow</subject>
<subject lang=en> Mechanical deformations</subject>
<subject lang=en> Gauss Seidel method</subject>
<subject lang=en> Nonlinear conjugate gradient method</subject>
<subject>[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>In this paper, we solve a problem describing the mechanical deformations of a porous medium in the presence of a monophasic linear flow or a two phase nonlinear flow with the purpose of modelizing subsidence of hydrocarbon reservoirs. An essential characteristics of this problem is that the mechanical deformation and the flow have different time scales. In petroleum industry, one uses different very efficient simulators for the flow problem and the mechanical deformations, which enables to handle complex models. Therefore it is necessary to be able to combine as efficiently as possible the exploitation of these simulators. We propose two alternative splitting approaches. The first one is the staggered algorithm used by engineers, which amounts to a Gauss-Seidel method in the one phase linear case. The second approach is based upon the preconditioned conjugate gradient method. We use a numerical multi-scale method in both of these algorithms. We compare these two approaches and we show that the preconditioned conjugate gradient algorithm is faster and more robust than the staggered algorithm. Applying the preconditioned conjugate gradient algorithm therefore seems to compensate for the fact that the inf-sup condition for the mixed discretization method is not satisfied when combining the simulators for the mechanical deformations and for the flow computations.</description>
<rights>http://creativecommons.org/licenses/by/</rights>
<date>2009</date>
</dc>
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