A nonlinear Stokes–Biot model for the interaction of a non-Newtonian fluid with poroelastic media
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 6, pp. 1915-1955.

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.

DOI : 10.1051/m2an/2019061
Classification : 76S05, 76D07, 74F10, 35M33, 65M60, 65M12
Mots-clés : Fluid-poroelastic structure interaction, Stokes–Biot model, fractured poroelastic media, non-Newtonian fluid
Ambartsumyan, Ilona 1 ; Ervin, Vincent J. 1 ; Nguyen, Truong 1 ; Yotov, Ivan 1

1 
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     title = {A nonlinear {Stokes{\textendash}Biot} model for the interaction of a {non-Newtonian} fluid with poroelastic media},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1915--1955},
     publisher = {EDP-Sciences},
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Ambartsumyan, Ilona; Ervin, Vincent J.; Nguyen, Truong; Yotov, Ivan. A nonlinear Stokes–Biot model for the interaction of a non-Newtonian fluid with poroelastic media. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 6, pp. 1915-1955. doi : 10.1051/m2an/2019061. http://www.numdam.org/articles/10.1051/m2an/2019061/

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