A nonlinear Stokes-Biot model for the interaction of a non-Newtonian fluid with poroelastic media
Provides a rigorous mathematical and numerical framework for coupled non-Newtonian fluid flow and poroelastic deformation, relevant to biomechanics and geophysics.
The paper develops and analyzes a nonlinear Stokes-Biot model for fluid-poroelastic interaction, proving existence, uniqueness, and finite element error estimates with numerical validation.
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.