Computational modeling of chemical transport in flow structure interactions in porous media

Coupled systems are frequently required to model observable phenomena beyond the basic level. Two applications of coupled systems are investigated in this work. One application is the modeling and analysis of the Richards equation to simulate water flow in the unsaturated zone in the presence of roots. This equation is coupled with the convection-diffusion equation to model chemical transport through the unsaturated zone. The movement of the water and chemical are observed in extended simulations. The second application is modeling chemical transport in the blood vessels and vessel walls. Since the blood flow determines how the chemical is transported, first the blood flow in the vessels and plasma flow in the vessel walls must be modeled. Here the two-dimensional transient Navier-Stokes equation to model the blood flow in the vessel is coupled with Darcy's Law to model the plasma flow through the vessel wall. Then the advection-diffusion equation is coupled with the velocities from the flows in the vessel and wall to model the transport of the chemical. Most of the difficulties in modeling this system lie in calculating the transient Navier-Stokes equation. Finite difference methodology is used in both applications for obtaining the numerical solution to the partial differential equations. Development of the analytical, numerical methods and computer implementation are discussed, and numerical results are included.