Open AccessAnalytic Element Modeling of Cylindrical Drains and Cylindrical Inhomogeneities in Steady Two‐Dimensional Unsaturated Flow
Author(s) -
Bakker Mark,
Nieber John L.
Publication year - 2004
Publication title -
vadose zone journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.036
H-Index - 81
ISSN - 1539-1663
DOI - 10.2136/vzj2004.1038
Subject(s) - analytic element method , vadose zone , flow (mathematics) , mechanics , porous medium , pressure head , analytic function , helmholtz free energy , boundary element method , coordinate system , hydraulic head , hydraulic conductivity , mathematics , saturation (graph theory) , mathematical analysis , geotechnical engineering , finite element method , geology , physics , geometry , thermodynamics , porosity , groundwater , combinatorics , soil water , soil science
The analytic element method, first developed for modeling flow in saturated porous media, is adapted to the solution of the governing equation for steady flow in unsaturated porous media. The governing equation for steady‐state unsaturated flow is made amenable to analytic element solution through transformation with the Kirchhoff integral, representation of the hydraulic conductivity by an exponential function of the pressure head, and use of a coordinate transformation. A number of analytic elements are available for the resulting modified Helmholtz equation; analytic element equations are presented for uniform flow, cylindrical drains, and cylindrical inhomogeneities. The analytic element solution allows for the analytic evaluation of the pressure head, saturation, and Darcy flux at any point in the vadose zone. The applicability of the analytic element method to simulate unsaturated flow is demonstrated by solving for several cases of steady flow in a region containing arbitrarily located cylindrical inhomogeneities, and for flow in a region containing one cylindrical inhomogeneity and two cylindrical drains.