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arXiv · 2109.15006

Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion

Bryan Gomez-Vargas·Kent-Andre Mardal·Ricardo Ruiz-Baier·Vegard Vinje
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Abstract

We introduce a stress/total-pressure formulation for poroelasticity that includes the coupling with steady nonlinear diffusion modified by stress. The nonlinear problem is written in mixed-primal form, coupling a perturbed twofold saddle-point system with an elliptic problem. The continuous formulation is analysed in the framework of abstract fixed-point theory and Fredholm alternative for compact operators. A mixed finite element method is proposed and its stability and convergence analysis are carried out. We also include a few illustrative numerical tests. The resulting model can be used to study waste removal in the brain parenchyma, where diffusion of a tracer alone or a combination of advection and diffusion are not sufficient to explain the alterations in rates of filtration observed in porous media samples.

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Bryan Gomez-Vargas, Kent-Andre Mardal, Ricardo Ruiz-Baier, Vegard Vinje. 2021-09-30. Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion. https://doi.org/10.1137/21m1449695

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