An analysis of groundwater flow in an infinite region with a sinusoidal top

P. N. Shivakumar; Joseph J. Williams; Qiang Ye; Chuanxiang Ji

doi:10.1080/01630560008816954

An analysis of groundwater flow in an infinite region with a sinusoidal top

P. N. Shivakumar, Joseph J. Williams, Qiang Ye, Chuanxiang Ji

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper we give a mathematical analysis with numerical computation for a groundwater flow problem described by an elliptic equation of the form ∇ · (e^dx∇φ(x, z)) = 0, d ≥ 0 in a semi-infinite vertical region bounded on top by a sloping sinusoidal curve, under given boundary conditions. φ(x, z) represents the hydraulic head and e^dx represents the relative hydraulic conductivity (or permeability). We reduce the problem to an infinite system of linear equations using the method of separation of variables and construction of a Grammian matrix. Truncation of this system yields an approximate solution that gives the best match on the top boundary. Computational results for some typical parameters are presented.

Original language	English
Pages (from-to)	263-271
Number of pages	9
Journal	Numerical Functional Analysis and Optimization
Volume	21
Issue number	1-2
DOIs	https://doi.org/10.1080/01630560008816954
State	Published - 2000

Keywords

Elliptic PDE
Groundwater flow
Modified bessel functions

ASJC Scopus subject areas

Analysis
Signal Processing
Computer Science Applications
Control and Optimization

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10.1080/01630560008816954

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title = "An analysis of groundwater flow in an infinite region with a sinusoidal top",

abstract = "In this paper we give a mathematical analysis with numerical computation for a groundwater flow problem described by an elliptic equation of the form ∇ · (edx∇φ(x, z)) = 0, d ≥ 0 in a semi-infinite vertical region bounded on top by a sloping sinusoidal curve, under given boundary conditions. φ(x, z) represents the hydraulic head and edx represents the relative hydraulic conductivity (or permeability). We reduce the problem to an infinite system of linear equations using the method of separation of variables and construction of a Grammian matrix. Truncation of this system yields an approximate solution that gives the best match on the top boundary. Computational results for some typical parameters are presented.",

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AU - Shivakumar, P. N.

AU - Williams, Joseph J.

AU - Ye, Qiang

AU - Ji, Chuanxiang

PY - 2000

Y1 - 2000

N2 - In this paper we give a mathematical analysis with numerical computation for a groundwater flow problem described by an elliptic equation of the form ∇ · (edx∇φ(x, z)) = 0, d ≥ 0 in a semi-infinite vertical region bounded on top by a sloping sinusoidal curve, under given boundary conditions. φ(x, z) represents the hydraulic head and edx represents the relative hydraulic conductivity (or permeability). We reduce the problem to an infinite system of linear equations using the method of separation of variables and construction of a Grammian matrix. Truncation of this system yields an approximate solution that gives the best match on the top boundary. Computational results for some typical parameters are presented.

AB - In this paper we give a mathematical analysis with numerical computation for a groundwater flow problem described by an elliptic equation of the form ∇ · (edx∇φ(x, z)) = 0, d ≥ 0 in a semi-infinite vertical region bounded on top by a sloping sinusoidal curve, under given boundary conditions. φ(x, z) represents the hydraulic head and edx represents the relative hydraulic conductivity (or permeability). We reduce the problem to an infinite system of linear equations using the method of separation of variables and construction of a Grammian matrix. Truncation of this system yields an approximate solution that gives the best match on the top boundary. Computational results for some typical parameters are presented.

KW - Elliptic PDE

KW - Groundwater flow

KW - Modified bessel functions

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JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

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ER -

An analysis of groundwater flow in an infinite region with a sinusoidal top

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Keywords

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