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<identifier>oai:HAL:hal-00730673v1</identifier>
<datestamp>2018-01-11</datestamp>
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<setSpec>subject:math</setSpec>
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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>Laminie, Jacques</creator>
<creator>Daim, Fatima Zahra</creator>
<creator>Hilhorst, Danielle</creator>
<creator>Eymard, Robert</creator>
<contributor>Laboratoire de Mathématiques Informatique et Applications (LAMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<contributor>Laboratoire EDP et analyse numérique ; Aucune</contributor>
<contributor>Laboratoire de Mathématiques d'Orsay (LM-Orsay) ; Université Paris-Sud - Paris 11 (UP11) - Centre National de la Recherche Scientifique (CNRS)</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-00730673</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00730673</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00730673</source>
<source>International Journal of Numerical Analysis and Modeling, Institute for Scientific Computing and Information, 2009, 5 (4), pp.635-658</source>
<language>en</language>
<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>The production of oil in soft highly compacted reservoirs produces a significant reduction in the pore space which in turn causes the surface to subside. The authors couple two simulators to model the mechanical deformations in the presence of a Darcy flow, both one- and two-phase. The simulators solve for flow in a porous medium using a finite volume method, and solve for the mechanical deformation of the porous media using a finite element method. The flow equations and the deformation equations are coupled using Biot's law. The authors use two different methods for the coupling: the first uses a staggered algorithm; the second is based on a preconditioned conjugate method. The authors use a multiscale method in both approaches. The authors show that the inf-sup condition is not satisfied, because of the mixed discretization which is done by using two separate simulators. The authors give convergence comparisons for the two methods for several examples. Two of the examples are for the linear problem (one-phase) where they know the exact solution and one is for the nonlinear problem (two-phase). In all cases, the preconditioned conjugate algorithm is faster and more robust, in particular when the inf-sup condition is not satisfied. In the nonlinear problem the authors state that the results agree with physical predictions but do not give actual empirical data. Finally, they show the effects of grid orientation on the nonlinear problem.</description>
<date>2009</date>
</dc>
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