American Institute of Mathematical Sciences

Advanced
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 & Heterogeneous Media, 2010, 5 (3) : 603-615. doi: 10.3934/nhm.2010.5.603
[1]

Donald L. Brown, Vasilena Taralova. A multiscale finite element method for Neumann problems in porous microstructures. Discrete & Continuous Dynamical Systems - S, 2016, 9 (5) : 1299-1326. doi: 10.3934/dcdss.2016052
[2]

Caterina Calgaro, Meriem Ezzoug, Ezzeddine Zahrouni. Stability and convergence of an hybrid finite volume-finite element method for a multiphasic incompressible fluid model. Communications on Pure & Applied Analysis, 2018, 17 (2) : 429-448. doi: 10.3934/cpaa.2018024
[3]

Christos V. Nikolopoulos, Georgios E. Zouraris. Numerical solution of a non-local elliptic problem modeling a thermistor with a finite element and a finite volume method. Conference Publications, 2007, 2007 (Special) : 768-778. doi: 10.3934/proc.2007.2007.768
[4]

Assyr Abdulle, Yun Bai, Gilles Vilmart. Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Discrete & Continuous Dynamical Systems - S, 2015, 8 (1) : 91-118. doi: 10.3934/dcdss.2015.8.91
[5]

Patrick Henning, Mario Ohlberger. The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift. Networks & Heterogeneous Media, 2010, 5 (4) : 711-744. doi: 10.3934/nhm.2010.5.711
[6]

Ying Liu, Yanping Chen, Yunqing Huang, Yang Wang. Two-grid method for semiconductor device problem by mixed finite element method and characteristics finite element method. Electronic Research Archive, , () : -. doi: 10.3934/era.2020095
[7]

Cornel M. Murea, H. G. E. Hentschel. A finite element method for growth in biological development. Mathematical Biosciences & Engineering, 2007, 4 (2) : 339-353. doi: 10.3934/mbe.2007.4.339
[8]

Martin Burger, José A. Carrillo, Marie-Therese Wolfram. A mixed finite element method for nonlinear diffusion equations. Kinetic & Related Models, 2010, 3 (1) : 59-83. doi: 10.3934/krm.2010.3.59
[9]

Junjiang Lai, Jianguo Huang. A finite element method for vibration analysis of elastic plate-plate structures. Discrete & Continuous Dynamical Systems - B, 2009, 11 (2) : 387-419. doi: 10.3934/dcdsb.2009.11.387
[10]

Binjie Li, Xiaoping Xie, Shiquan Zhang. New convergence analysis for assumed stress hybrid quadrilateral finite element method. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2831-2856. doi: 10.3934/dcdsb.2017153
[11]

Kun Wang, Yinnian He, Yueqiang Shang. Fully discrete finite element method for the viscoelastic fluid motion equations. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 665-684. doi: 10.3934/dcdsb.2010.13.665
[12]

So-Hsiang Chou. An immersed linear finite element method with interface flux capturing recovery. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2343-2357. doi: 10.3934/dcdsb.2012.17.2343
[13]

Hao Wang, Wei Yang, Yunqing Huang. An adaptive edge finite element method for the Maxwell's equations in metamaterials. Electronic Research Archive, 2020, 28 (2) : 961-976. doi: 10.3934/era.2020051
[14]

Qingping Deng. A nonoverlapping domain decomposition method for nonconforming finite element problems. Communications on Pure & Applied Analysis, 2003, 2 (3) : 297-310. doi: 10.3934/cpaa.2003.2.297
[15]

Runchang Lin. A robust finite element method for singularly perturbed convection-diffusion problems. Conference Publications, 2009, 2009 (Special) : 496-505. doi: 10.3934/proc.2009.2009.496
[16]

Xiu Ye, Shangyou Zhang, Peng Zhu. A weak Galerkin finite element method for nonlinear conservation laws. Electronic Research Archive, , () : -. doi: 10.3934/era.2020097
[17]

Eric Chung, Yalchin Efendiev, Ke Shi, Shuai Ye. A multiscale model reduction method for nonlinear monotone elliptic equations in heterogeneous media. Networks & Heterogeneous Media, 2017, 12 (4) : 619-642. doi: 10.3934/nhm.2017025
[18]

Nan Li, Song Wang, Shuhua Zhang. Pricing options on investment project contraction and ownership transfer using a finite volume scheme and an interior penalty method. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1349-1368. doi: 10.3934/jimo.2019006
[19]

Stefan Berres, Ricardo Ruiz-Baier, Hartmut Schwandt, Elmer M. Tory. An adaptive finite-volume method for a model of two-phase pedestrian flow. Networks & Heterogeneous Media, 2011, 6 (3) : 401-423. doi: 10.3934/nhm.2011.6.401
[20]

Hatim Tayeq, Amal Bergam, Anouar El Harrak, Kenza Khomsi. Self-adaptive algorithm based on a posteriori analysis of the error applied to air quality forecasting using the finite volume method. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020400

2019 Impact Factor: 1.053

Tools

Metrics

  • PDF downloads (23)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences