Robust iterative schemes for non-linear poromechanics |
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| Authors: | Manuel Borregales Florin A Radu Kundan Kumar Jan M Nordbotten |
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| Institution: | 1.Department of Mathematics,University of Bergen,Bergen,Norway;2.Department of Civil and Environmental Engineering,Princeton University,Princeton,USA |
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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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