Mathematical and numerical modeling of flow and transport in fluid–poroelastic structure interactionWang, Xing (2022) Mathematical and numerical modeling of flow and transport in fluid–poroelastic structure interaction. Doctoral Dissertation, University of Pittsburgh. (Unpublished)
AbstractThe thesis focuses on the analysis and simulation of fluid–poroelastic structure interaction (FPSI), which describes the interaction between free fluid and a neighboring poroelastic medium through an interface. The Stokes or time-dependent Navier-Stokes equations govern the flow in the fluid region. The Biot system describes the flow within the poroelastic media and the structure deformation. The two regions are coupled via mass conservation, balance of normal stress, balance of momentum, and the Beaver-Joseph-Saffman slip with friction condition. A mixed Darcy formulation is employed, and a pressure Lagrange multiplier on interface is introduced to impose weakly continuity of flux. The Stokes–Biot model is further coupled with an advection-diffusion transport equation for the solute concentration. First, we discuss a Lagrange multiplier method for the fully dynamic Navier-Stokes–Biot model. The existence, uniqueness, and stability of the solution are obtained. We further study the well-posedness of a fully discrete scheme approximating the model based on suitable finite element spaces and derive error estimates. Numerical simulations illustrate the order of convergence and the feasibility of the numerical method to model a benchmark problem involving Newtonian blood flow. We extend the Newtonian model to a non-Newtonian fluid via the Carreau-Yasuda model for shear-thinning rheology. We study the effect of poroelasticity of blood vessels and non- Newtonian blood rheology on important clinical markers such as wall shear stress and relative residence time. We further conduct numerical experiments illustrating the blood flow in stenotic vessels. Finally, we discuss a two-way coupled Stokes–Biot–transport model. The convective term in the transport equation, which depends on the fluid velocity and the concentration- Share
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