Full Record

Author | McGee, Shelly M. |

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

URL | http://hdl.handle.net/2346/14053 |

Publication Date | 2007 |

Date Accessioned | 2016-11-14 23:16:11 |

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 | 2020-04-09 |

Date Indexed | 2020-04-11 |

Sample Search Hits | Sample Images

…*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…

…2.25 Watering daily for two hours: Day 2. . . . . . . . . . . . . . . . . . .
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2.26 Watering daily for two hours: Day 3. . . . . . . . . . . . . . . . . . .
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*Texas* *Tech* *University*, S. McGee, August 2007
2.27 Watering daily for two hours…

…Ωw . . . . . . . . . . . . . . . . . . .
50
3.11 Direction of flow in Ωf and Ωw . . . . . . . . . . . . . . . . . . . . . .
50
3.12 Concentration on Ωf . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
viii
*Texas* *Tech* *University*, S…

…52
4.1
55
Single domain used in the error estimates. . . . . . . . . . . . . . . .
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*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
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*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.
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*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
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*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
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*Texas* *Tech* *University*, S. McGee, August 2007
2
10
0…