Robust iterative schemes for non-linear poromechanics
For researchers in computational poromechanics, this provides rigorous convergence guarantees for nonlinear extensions of standard splitting and monolithic methods.
This paper extends Biot's poromechanics model to nonlinear fluid flow and mechanical deformation, proposing two iterative schemes (a splitting algorithm and a monolithic L-scheme) with proven convergence, validated through numerical examples.
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.