Abstract: We study the coupled system of the flow and transport problem. In this paper, the Stokes equations are adopted to govern the fluids region; for the poroelastic region, the Biot system is utilized; for the transport of species within the fluids, we use an advection-diffusion equation. Equilibrium and kinematic conditions are imposed on the interface between the fluid and poroelastic media. And the continuity of flux on the fluid-structure interface is imposed via a Lagrange multiplier. This model is fully coupled and nonlinear due to the convective transport term and the nonlinear viscosity. To address the stability and convergence of the coupled system, we first use a Galerkin method and a priori estimates to obtain the well-posedness of a linearized formulation. Next, a fixed-point iteration procedure is utilized to study the stability and convergence of the original nonlinear problem. The error analysis is performed for the semi-discrete continuous-in-time formulation. A series of computational experiments are conducted to confirm the theoretical convergence rate and to explore the feasibility of the method to model the physical flow and transport phenomena.
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