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Mathematical modeling of goundwater flow with the effects of advection and dispersion in a porous medium

Groundwater is one of the most important fresh water resources in our earth .This dissertation presents the mathematical model of groundwater flow with the effect of advection and dispersion in a porous medium. The purpose of this dissertation is to review in detail the one-dimensional advection-dis...

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Main Author: Samsudin, Adam
Format: Thesis
Language:English
Published: 2014
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/43942/1/AdamShamsudinMFS2014.pdf
http://eprints.utm.my/id/eprint/43942/
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spelling my.utm.439422017-09-11T06:12:02Z http://eprints.utm.my/id/eprint/43942/ Mathematical modeling of goundwater flow with the effects of advection and dispersion in a porous medium Samsudin, Adam QA Mathematics Groundwater is one of the most important fresh water resources in our earth .This dissertation presents the mathematical model of groundwater flow with the effect of advection and dispersion in a porous medium. The purpose of this dissertation is to review in detail the one-dimensional advection-dispersion equation (ADE) for two different groundwater problems that is continuous injection and instantaneous injection. In this study, we are formulating a one dimensional mathematical model of a groundwater flow with only the effect of advection and dispersion. We are using Laplace transform to solve the advection dispersion equation for both cases but in a different way. For continuous injection we introduce dependent variable,C(x,t)=r(x,t)exp(ux-u2t) and apply the Duhamel’s theorem. While for instantaneous injection, after transform the general equation into Laplace form we change it into characteristic form and solve it using by applied the boundary condition. Lastly, we solved the continuous injection problem used numerical method via Mathematica programming. Results of the advection dispersion model of this problem are presented by the graphical figures. 2014-01 Thesis NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/43942/1/AdamShamsudinMFS2014.pdf Samsudin, Adam (2014) Mathematical modeling of goundwater flow with the effects of advection and dispersion in a porous medium. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science.
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Samsudin, Adam
Mathematical modeling of goundwater flow with the effects of advection and dispersion in a porous medium
description Groundwater is one of the most important fresh water resources in our earth .This dissertation presents the mathematical model of groundwater flow with the effect of advection and dispersion in a porous medium. The purpose of this dissertation is to review in detail the one-dimensional advection-dispersion equation (ADE) for two different groundwater problems that is continuous injection and instantaneous injection. In this study, we are formulating a one dimensional mathematical model of a groundwater flow with only the effect of advection and dispersion. We are using Laplace transform to solve the advection dispersion equation for both cases but in a different way. For continuous injection we introduce dependent variable,C(x,t)=r(x,t)exp(ux-u2t) and apply the Duhamel’s theorem. While for instantaneous injection, after transform the general equation into Laplace form we change it into characteristic form and solve it using by applied the boundary condition. Lastly, we solved the continuous injection problem used numerical method via Mathematica programming. Results of the advection dispersion model of this problem are presented by the graphical figures.
format Thesis
author Samsudin, Adam
author_facet Samsudin, Adam
author_sort Samsudin, Adam
title Mathematical modeling of goundwater flow with the effects of advection and dispersion in a porous medium
title_short Mathematical modeling of goundwater flow with the effects of advection and dispersion in a porous medium
title_full Mathematical modeling of goundwater flow with the effects of advection and dispersion in a porous medium
title_fullStr Mathematical modeling of goundwater flow with the effects of advection and dispersion in a porous medium
title_full_unstemmed Mathematical modeling of goundwater flow with the effects of advection and dispersion in a porous medium
title_sort mathematical modeling of goundwater flow with the effects of advection and dispersion in a porous medium
publishDate 2014
url http://eprints.utm.my/id/eprint/43942/1/AdamShamsudinMFS2014.pdf
http://eprints.utm.my/id/eprint/43942/
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score 13.211869

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