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arXiv · 1702.00328

Robust iterative schemes for non-linear poromechanics

Manuel Borregales·Florin A. Radu·Kundan Kumar·Jan M. Nordbotten
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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. 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 is shown rigorously. Illustrative numerical examples are presented to confirm the applicability of the schemes and validate the theoretical results.

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Manuel Borregales, Florin A. Radu, Kundan Kumar, Jan M. Nordbotten. 2017-02-01. Robust iterative schemes for non-linear poromechanics. https://arxiv.org/abs/1702.00328

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