American Institute of Mathematical Sciences

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September  2010, 5(3): 603-615. doi: 10.3934/nhm.2010.5.603

Application of a coupled FV/FE multiscale method to cement media

Thomas Abballe 1, , Grégoire Allaire 2, , Éli Laucoin 1, and  Philippe Montarnal 1,

1. 

CEA Saclay, DEN/DM2S/SFME/LSET Bat 454, 91191 Gif-sur-Yvette Cedex, France, France, France
2. 

Conseiller Scientifique du DM2S – CEA Saclay, Centre de Mathématiques Appliquées – École Polytechnique, 91128 Palaiseau Cedex, France

Received  January 2010 Revised  June 2010 Published  July 2010

We present here some results provided by a multiscale resolution method using both Finite Volumes and Finite Elements. This method is aimed at solving very large diffusion problems with highly oscillating coefficients. As an illustrative example, we simulate models of cement media, where very strong variations of diffusivity occur. As a by-product of our simulations, we compute the effective diffusivities of these media. After a short introduction, we present a theorical description of our method. Numerical experiments on a two dimensional cement paste are presented subsequently. The third section describes the implementation of our method in the calculus code MPCube and its application to a sample of mortar. Finally, we discuss strengths and weaknesses of our method, and present our future works on this topic.
Keywords: finite element method, finite volume method, cement media., multiscale method.
Mathematics Subject Classification: 74Q05, 65N3.
Citation: Thomas Abballe, Grégoire Allaire, Éli Laucoin, Philippe Montarnal. Application of a coupled FV/FE multiscale method to cement media. Networks and Heterogeneous Media, 2010, 5 (3) : 603-615. doi: 10.3934/nhm.2010.5.603
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