Drawdown in prolate spheroidal-spherical coordinates obtained via Green's function and perturbation methods

被引:20
作者
Atangana, Abdon [1 ]
机构
[1] Univ Orange Free State, Inst Groundwater Studies, Fac Nat & Agr Sci, Bloemfontein, South Africa
关键词
Groundwater flow equation; Prolate spheroidal coordinates; Asymptotic expansion; Green's function; Numerical errors; SCATTERING; FLOW;
D O I
10.1016/j.cnsns.2013.09.031
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
When investigating aquifer behaviour it is important to note that there exists a close relationship between the geometrical properties of the aquifer and the behaviour of the solution. In this paper our concern is to solve the flow equation described by prolate spheroidal coordinates by means of perturbation and the Green's function method, where the spheroid is considered to be a perturbation of a sphere. We transformed the spheroidal coordinates to spherical polar coordinates in the limit, as the shape factor tends to zero. The new groundwater flow equation is solved via an asymptotic parameter expansion and the Green's function method. The approximate solution of the new equation is compared with experimental data from real world. To take into account the error committed while approximating, we estimate the error in the asymptotic expansion. The error functions obtained suggest that the error would be very small for the shape factor tending to zero if the first two terms of the expansion are taken as an approximation. (C) 2013 Elsevier B.V. All rights reserved.
引用
收藏
页码:1259 / 1269
页数:11
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