Parameter-robust methods for the Biot–Stokes interfacial coupling without Lagrange multipliers

In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A five-field mixed-primal finite element scheme is proposed solving...

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Bibliographic Details
Published in:Journal of computational physics 2022-10, Vol.467, p.111464, Article 111464
Main Authors: Boon, Wietse M., Hornkjøl, Martin, Kuchta, Miroslav, Mardal, Kent-André, Ruiz-Baier, Ricardo
Format: Article
Language:English
Subjects:
Biot-Stokes coupling
Brain poromechanics
Computational physics
Coupling
Fluid pressure
Fluid-structure interaction
Formability
Free flow
Interaction models
Lagrange multiplier
Metric space
Mixed finite elements
Newtonian fluids
Operator preconditioning
Parameter robustness
Porous media
Robustness
Saddle points
Total pressure
Transmission problem
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Summary:In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A five-field mixed-primal finite element scheme is proposed solving for Stokes velocity-pressure and Biot displacement-total pressure-fluid pressure. Adequate inf-sup conditions are derived, and one of the distinctive features of the formulation is that its stability is established robustly in all material parameters. We propose robust preconditioners for this perturbed saddle-point problem using appropriately weighted operators in fractional Sobolev and metric spaces at the interface. The performance is corroborated by several test cases, including the application to interfacial flow in the brain.
ISSN:0021-9991
1090-2716
1090-2716
DOI:10.1016/j.jcp.2022.111464