Multiscale finite-element method for linear elastic geomechanics

Journal Article (2016)
Research Group
Reservoir Engineering
Copyright
© 2016 N Castelletto, H. Hajibeygi, HA Tchelepi
DOI related publication
https://doi.org/10.1016/j.jcp.2016.11.044
More Info
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Publication Year
2016
Language
English
Copyright
© 2016 N Castelletto, H. Hajibeygi, HA Tchelepi
Research Group
Reservoir Engineering
Volume number
331
Pages (from-to)
337-356
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Abstract

The demand for accurate and efficient simulation of geomechanical effects is widely increasing in the geoscience community. High resolution characterizations of the mechanical properties of subsurface formations are essential for improving modeling predictions. Such detailed descriptions impose severe computational challenges and motivate the development of multiscale solution strategies. We propose a multiscale solution framework for the geomechanical equilibrium problem of heterogeneous porous media based on the finite-element method. After imposing a coarsescale grid on the given fine-scale problem, the coarse-scale basis functions are obtained by solving local equilibrium problems within coarse elements. These basis functions form the restriction and prolongation operators used to obtain the coarse-scale system for the displacement-vector. Then, a two-stage preconditioner that couples the multiscale system with a smoother is derived for the iterative solution of the fine-scale linear system. Various numerical experiments are presented to demonstrate accuracy and robustness of the method.

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