Computational Multiscale Methods for Linear Heterogeneous Poroelasticity

Computational Multiscale Methods for Linear Heterogeneous Poroelasticity

Year:    2020

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

Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1902-m2018-0186

Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 41–57

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Poroelasticity Heterogeneous media Numerical homogenization Multiscale methods.

Author Details

Robert Altmann

Eric T. Chung

Roland Maier

Daniel Peterseim

Sai-Mang Pun