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Title Computational modeling of chemical transport in flow structure interactions in porous media
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Publication Date
Date Accessioned
University/Publisher Texas Tech University
Abstract 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.
Subjects/Keywords Finite differences; Additive schwarz; Nonlinear
Contributors Seshaiyer, Padmanabhan (Committee Chair); Ibragimov, Akif (committee member); Allen, Edward J. (committee member); Aulisa, Eugenio (committee member)
Language en
Rights Unrestricted.
Country of Publication us
Record ID handle:2346/14053
Repository tdl
Date Retrieved
Date Indexed 2020-04-11

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Texas Tech University, S. McGee, August 2007 LIST OF FIGURES 2.1 Relationship between h and K(h) . . . . . . . . . . . . . . . . . . . . 5 2.2 Relationship between h and θ . . . . . . . . . . . . . . . . . . . . . . 6 2.3…

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…52 4.1 55 Single domain used in the error estimates. . . . . . . . . . . . . . . . ix Texas Tech University, S. McGee, August 2007 CHAPTER I INTRODUCTION The hydrologic cycle is the cycle of water on Earth. There are two types of water, ground…

…roots [11]. This is a desirable process if the chemical 1 Texas Tech University, S. McGee, August 2007 is used by the plant, like nitrogen. But in the case of perchlorate, the plant does not use the perchlorate, so the perchlorate remains in…

…validated in Chapter IV. Followed by conclusions and future work. 2 Texas Tech University, S. McGee, August 2007 CHAPTER II CHEMICAL TRANSPORT IN POROUS MEDIA There are many kinds of aquifers, the aquifer considered in this chapter is an unconfined…

…was developed by L. A. Richards in 1931 [20], and the 3 Texas Tech University, S. McGee, August 2007 equation bears his name. The Richards equation with a sink term is ∂θ(h) ∂ = ∂t ∂x K(h) ∂h − sin(A) ∂x…

…empirical constants that vary depending on soil, and m is given by m = 1 − 1 N [17, 21]. The characteristic curve for a specific soil is displayed in figure 2.1. This graph displays the 4 Texas Tech University, S. McGee, August 2007 2 10 0…

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