A nonlinear Stokes-Biot model for the interaction of a non-Newtonian fluid with poroelastic media

TL;DR

This paper introduces a nonlinear Stokes-Biot model to simulate the interaction between a non-Newtonian fluid and poroelastic media, providing theoretical analysis and numerical validation of the model's accuracy.

Contribution

It develops a coupled nonlinear model for fluid-poroelastic interactions, including existence, uniqueness, and error analysis, with finite element approximation and numerical experiments.

Findings

Proved existence and uniqueness of solutions.

Established error bounds for the finite element method.

Validated the model through numerical experiments.

Abstract

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.