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Volume 38, Issue 1
Computational Multiscale Methods for Linear Heterogeneous Poroelasticity

Robert Altmann, Eric T. Chung, Roland Maier, Daniel Peterseim & Sai-Mang Pun

DOI: 10.4208/jcm.1902-m2018-0186

J. Comp. Math., 38 (2020), pp. 41-57.

Published online: 2020-02

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  • Abstract

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough numerical treatment. In this paper, we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity. Therein, local corrector problems are constructed in line with the static equations, whereas we propose to consider the full system. This allows benefiting from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure. We prove the optimal first-order convergence of this method and verify the result by numerical experiments.

  • Keywords

Poroelasticity, Heterogeneous media, Numerical homogenization, Multiscale methods.

  • AMS Subject Headings

65M12, 65M60, 76S05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

robert.altmann@math.uni-augsburg.de (Robert Altmann)

tschung@math.cuhk.edu.hk (Eric T. Chung)

roland.maier@math.uni-augsburg.de (Roland Maier)

daniel.peterseim@math.uni-augsburg.de (Daniel Peterseim)

smpun@math.tamu.edu (Sai-Mang Pun)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-41, author = {Altmann , RobertChung , Eric T.Maier , RolandPeterseim , Daniel and Pun , Sai-Mang}, title = {Computational Multiscale Methods for Linear Heterogeneous Poroelasticity}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {1}, pages = {41--57}, abstract = {

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough numerical treatment. In this paper, we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity. Therein, local corrector problems are constructed in line with the static equations, whereas we propose to consider the full system. This allows benefiting from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure. We prove the optimal first-order convergence of this method and verify the result by numerical experiments.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1902-m2018-0186}, url = {http://global-sci.org/intro/article_detail/jcm/13684.html} }
TY - JOUR T1 - Computational Multiscale Methods for Linear Heterogeneous Poroelasticity AU - Altmann , Robert AU - Chung , Eric T. AU - Maier , Roland AU - Peterseim , Daniel AU - Pun , Sai-Mang JO - Journal of Computational Mathematics VL - 1 SP - 41 EP - 57 PY - 2020 DA - 2020/02 SN - 38 DO - http://doi.org/10.4208/jcm.1902-m2018-0186 UR - https://global-sci.org/intro/article_detail/jcm/13684.html KW - Poroelasticity, Heterogeneous media, Numerical homogenization, Multiscale methods. AB -

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough numerical treatment. In this paper, we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity. Therein, local corrector problems are constructed in line with the static equations, whereas we propose to consider the full system. This allows benefiting from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure. We prove the optimal first-order convergence of this method and verify the result by numerical experiments.

Altmann , RobertChung , Eric T.Maier , RolandPeterseim , Daniel and Pun , Sai-Mang. (2020). Computational Multiscale Methods for Linear Heterogeneous Poroelasticity. Journal of Computational Mathematics. 38 (1). 41-57. doi:10.4208/jcm.1902-m2018-0186
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