Variational analysis for simulating free-surface flows in a porous medium
A variational formulation has been developed to solve a parabolic partial differential equation describing free-surface flows in a porous medium. The variational finite element method is used to obtain a discrete form of equations for a two-dimensional domain. The matrix characteristics and the sta...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X03301147 |
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| _version_ | 1832556518486048768 |
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| author | Shabbir Ahmed Charles Collins |
| author_facet | Shabbir Ahmed Charles Collins |
| author_sort | Shabbir Ahmed |
| collection | DOAJ |
| description | A variational formulation has been developed to solve a parabolic partial differential equation describing free-surface flows in a porous medium. The variational finite element method
is used to obtain a discrete form of equations for a two-dimensional domain. The matrix characteristics and the stability criteria have been investigated to develop a stable numerical algorithm for solving the governing equation. A computer programme has been written to solve a symmetric positive definite system obtained from the variational finite element analysis. The system of equations is solved using the conjugate gradient method. The solution generates time-varying hydraulic heads in the subsurface. The interfacing free surface between the unsaturated and saturated zones in the variably saturated domain is located, based on the computed hydraulic heads. Example problems are investigated. The finite element solutions are compared with the exact solutions for the example problems. The numerical characteristics of the finite element solution method are also investigated using the example problems. |
| format | Article |
| id | doaj-art-5675fdf33e6442bfae7ff6f46e631b5e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5675fdf33e6442bfae7ff6f46e631b5e2025-02-03T05:45:10ZengWileyJournal of Applied Mathematics1110-757X1687-00422003-01-012003837739610.1155/S1110757X03301147Variational analysis for simulating free-surface flows in a porous mediumShabbir Ahmed0Charles Collins1Big Cypress Basin, South Florida Water Management District, 6089 Janes Lane, Naples 34109, FL, USADepartment of Mathematics, University of Tennessee, 121 Ayres Hall, 1403 Circle Drive, Knoxville 37996, TN, USAA variational formulation has been developed to solve a parabolic partial differential equation describing free-surface flows in a porous medium. The variational finite element method is used to obtain a discrete form of equations for a two-dimensional domain. The matrix characteristics and the stability criteria have been investigated to develop a stable numerical algorithm for solving the governing equation. A computer programme has been written to solve a symmetric positive definite system obtained from the variational finite element analysis. The system of equations is solved using the conjugate gradient method. The solution generates time-varying hydraulic heads in the subsurface. The interfacing free surface between the unsaturated and saturated zones in the variably saturated domain is located, based on the computed hydraulic heads. Example problems are investigated. The finite element solutions are compared with the exact solutions for the example problems. The numerical characteristics of the finite element solution method are also investigated using the example problems.http://dx.doi.org/10.1155/S1110757X03301147 |
| spellingShingle | Shabbir Ahmed Charles Collins Variational analysis for simulating free-surface flows in a porous medium Journal of Applied Mathematics |
| title | Variational analysis for simulating free-surface flows in a porous medium |
| title_full | Variational analysis for simulating free-surface flows in a porous medium |
| title_fullStr | Variational analysis for simulating free-surface flows in a porous medium |
| title_full_unstemmed | Variational analysis for simulating free-surface flows in a porous medium |
| title_short | Variational analysis for simulating free-surface flows in a porous medium |
| title_sort | variational analysis for simulating free surface flows in a porous medium |
| url | http://dx.doi.org/10.1155/S1110757X03301147 |
| work_keys_str_mv | AT shabbirahmed variationalanalysisforsimulatingfreesurfaceflowsinaporousmedium AT charlescollins variationalanalysisforsimulatingfreesurfaceflowsinaporousmedium |