Volume 53, Number 6, November-December 2019
|Page(s)||1915 - 1955|
|Published online||24 October 2019|
A nonlinear Stokes–Biot model for the interaction of a non-Newtonian fluid with poroelastic media
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
2 Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
3 Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA
* Corresponding author: firstname.lastname@example.org
Accepted: 6 August 2019
We develop and analyze a model for the interaction of a quasi-Newtonian free fluid with a poroelastic medium. The flow in the fluid region is described by the nonlinear Stokes equations and in the poroelastic medium by the nonlinear quasi-static Biot model. Equilibrium and kinematic conditions are imposed on the interface. We establish existence and uniqueness of a solution to the weak formulation and its semidiscrete continuous-in-time finite element approximation. We present error analysis, complemented by numerical experiments.
Mathematics Subject Classification: 76S05 / 76D07 / 74F10 / 35M33 / 65M60 / 65M12
Key words: Fluid-poroelastic structure interaction / Stokes–Biot model / fractured poroelastic media / non-Newtonian fluid
© EDP Sciences, SMAI 2019
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