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Robust iterative schemes for non-linear poromechanics

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Abstract

We consider a non-linear extension of Biot’s model for poromechanics, wherein both the fluid flow and mechanical deformation are allowed to be non-linear. Specifically, we study the case when the volumetric stress and the fluid density are non-linear functions satisfying certain assumptions. We perform an implicit discretization in time (backward Euler) and propose two iterative schemes for solving the non-linear problems appearing within each time step: a splitting algorithm extending the undrained split and fixed stress methods to non-linear problems, and a monolithic L-scheme. The convergence of both schemes are shown rigorously. Illustrative numerical examples are presented to confirm the applicability of the schemes and validate the theoretical results.

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Funding

The research was supported by the University of Bergen in cooperation with the FME-SUCCESS center (grant 193825/S60) funded by the Research Council of Norway. The work has also been partly supported by the following: the NFR-DAADppp grant 255715, the NFR-Toppforsk project 250223, the NRC-CHI grant 255510, and the NRC-IMMENS grant 255426.

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Authors and Affiliations

  1. Department of Mathematics, University of Bergen, Bergen, Norway

    Manuel Borregales, Florin A. Radu, Kundan Kumar & Jan M. Nordbotten

  2. Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA

    Jan M. Nordbotten

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  1. Manuel Borregales
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  2. Florin A. Radu
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  3. Kundan Kumar
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  4. Jan M. Nordbotten
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Correspondence to Manuel Borregales.

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Borregales, M., Radu, F.A., Kumar, K. et al. Robust iterative schemes for non-linear poromechanics. Comput Geosci 22, 1021–1038 (2018). https://doi.org/10.1007/s10596-018-9736-6

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