Integral equation techniques in groundwater flow

In this study, integral equation techniques are developed to solve two different types of groundwater flow problem. The first formulation, based on the Cauchy integral theorem, is used to obtain numerical solutions for unsteady, two-dimensional flow through a homogeneous, isotropic embankment. Free...

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Main Author: Mitchell, Philip H.
Language:en
Published: University of Canterbury. Civil Engineering 2013
Online Access:http://hdl.handle.net/10092/7690
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spelling ndltd-canterbury.ac.nz-oai-ir.canterbury.ac.nz-10092-76902015-03-30T15:29:34ZIntegral equation techniques in groundwater flowMitchell, Philip H.In this study, integral equation techniques are developed to solve two different types of groundwater flow problem. The first formulation, based on the Cauchy integral theorem, is used to obtain numerical solutions for unsteady, two-dimensional flow through a homogeneous, isotropic embankment. Free surface profiles following instantaneous drawdown of an upstream reservoir are presented in dimensionless form. The results from an unsteady, parallel-plate, viscous-flow experiment are included to check the accuracy of one of the numerical solutions and to show the limitations of the experimental approach. The numerical results are also compared with the simpler results obtained by making the Dupuit approximation, the inadequacies of which are also discussed. In aquifers where horizontal dimensions are orders of magnitude greater than vertical dimensions the Dupuit approximation is valid, and a three-dimensional problem is reduced to two dimensions in the horizontal plane. An integral equation technique for solving such problems is presented, in which time-dependent fundamental solutions of the governing partial differential equation are distributed around the flow boundary so that the initial and boundary conditions are satisfied. Two numerical methods of solving the integral equation are compared for a wide range of problems in both homogeneous and zoned regions. Each region may, or may not, contain wells. Comparisons with the finite-difference method are also made for certain problems.University of Canterbury. Civil Engineering2013-05-13T08:32:06Z2013-05-13T08:32:06Z1984Electronic thesis or dissertationTexthttp://hdl.handle.net/10092/7690enNZCUCopyright Philip H. Mitchellhttp://library.canterbury.ac.nz/thesis/etheses_copyright.shtml
collection NDLTD
language en
sources NDLTD
description In this study, integral equation techniques are developed to solve two different types of groundwater flow problem. The first formulation, based on the Cauchy integral theorem, is used to obtain numerical solutions for unsteady, two-dimensional flow through a homogeneous, isotropic embankment. Free surface profiles following instantaneous drawdown of an upstream reservoir are presented in dimensionless form. The results from an unsteady, parallel-plate, viscous-flow experiment are included to check the accuracy of one of the numerical solutions and to show the limitations of the experimental approach. The numerical results are also compared with the simpler results obtained by making the Dupuit approximation, the inadequacies of which are also discussed. In aquifers where horizontal dimensions are orders of magnitude greater than vertical dimensions the Dupuit approximation is valid, and a three-dimensional problem is reduced to two dimensions in the horizontal plane. An integral equation technique for solving such problems is presented, in which time-dependent fundamental solutions of the governing partial differential equation are distributed around the flow boundary so that the initial and boundary conditions are satisfied. Two numerical methods of solving the integral equation are compared for a wide range of problems in both homogeneous and zoned regions. Each region may, or may not, contain wells. Comparisons with the finite-difference method are also made for certain problems.
author Mitchell, Philip H.
spellingShingle Mitchell, Philip H.
Integral equation techniques in groundwater flow
author_facet Mitchell, Philip H.
author_sort Mitchell, Philip H.
title Integral equation techniques in groundwater flow
title_short Integral equation techniques in groundwater flow
title_full Integral equation techniques in groundwater flow
title_fullStr Integral equation techniques in groundwater flow
title_full_unstemmed Integral equation techniques in groundwater flow
title_sort integral equation techniques in groundwater flow
publisher University of Canterbury. Civil Engineering
publishDate 2013
url http://hdl.handle.net/10092/7690
work_keys_str_mv AT mitchellphiliph integralequationtechniquesingroundwaterflow
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