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: email@example.com
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.