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Networks and Heterogeneous Media

2010, Volume 5, Issue 3: 603-615. doi: 10.3934/nhm.2010.5.603
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Application of a coupled FV/FE multiscale method to cement media

  • 1.
    CEA Saclay, DEN/DM2S/SFME/LSET Bat 454, 91191 Gif-sur-Yvette Cedex
  • 2.
    Conseiller Scientifique du DM2S – CEA Saclay, Centre de Mathématiques Appliquées – École Polytechnique, 91128 Palaiseau Cedex
  • Received: 01 January 2010 Revised: 01 June 2010

  • 74Q05, 65N30.

  • 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.

    Citation: Thomas Abballe, Grégoire Allaire, Éli Laucoin, Philippe Montarnal. Application of a coupled FV/FE multiscale method to cement media[J]. Networks and Heterogeneous Media, 2010, 5(3): 603-615. doi: 10.3934/nhm.2010.5.603

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  • 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.


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  • © 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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