A multistep fundamental solution scheme for modeling groundwater flow
A new numerical scheme for solving transient pressure in a confined aquifer is presented. It is based on the fundamental solution method (FSM) and it combines free Green functions, superposition principle, and singular value decomposition (SVD) method to obtain an efficient computational algorithm t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Universidad de Costa Rica
2009-02-01
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| Series: | Revista de Matemática: Teoría y Aplicaciones |
| Online Access: | https://revistas.ucr.ac.cr/index.php/matematica/article/view/1423 |
| _version_ | 1797705640440758272 |
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| author | Juan M. Guevara-Jordan Carmen M. Da Silva-Rodrigues |
| author_facet | Juan M. Guevara-Jordan Carmen M. Da Silva-Rodrigues |
| author_sort | Juan M. Guevara-Jordan |
| collection | DOAJ |
| description | A new numerical scheme for solving transient pressure in a confined aquifer is
presented. It is based on the fundamental solution method (FSM) and it combines
free Green functions, superposition principle, and singular value decomposition (SVD)
method to obtain an efficient computational algorithm to approximate unsteady pressure
in general two dimensional groundwater problems. Its mathematical formulation
avoids integral equations, is meshfree, and its new multistep approach provides very
accurate approximation of full transient aquifer pressure along any period of time.
The new scheme was validated with synthetic aquifers problems with constant and
variable well rates. Its applications to arbitrary shaped aquifer with multiple wells
is developed and analyzed. Numerical results gave evidence that the new scheme
is a versatile tool and an alternative choice to boundary element methods to solve
groundwater problems.
Keywords: multistep, meshless, fundamental solution method, free Green function, singular
value decomposition. |
| first_indexed | 2024-03-12T05:40:23Z |
| format | Article |
| id | doaj.art-3fc11671e09c4674b5e281289688ae5a |
| institution | Directory Open Access Journal |
| issn | 2215-3373 |
| language | English |
| last_indexed | 2024-03-12T05:40:23Z |
| publishDate | 2009-02-01 |
| publisher | Universidad de Costa Rica |
| record_format | Article |
| series | Revista de Matemática: Teoría y Aplicaciones |
| spelling | doaj.art-3fc11671e09c4674b5e281289688ae5a2023-09-03T06:08:44ZengUniversidad de Costa RicaRevista de Matemática: Teoría y Aplicaciones2215-33732009-02-0116113714710.15517/rmta.v16i1.14231355A multistep fundamental solution scheme for modeling groundwater flowJuan M. Guevara-Jordan0Carmen M. Da Silva-Rodrigues1Universidad Central de Venezuela, Escuela de MatemáticasUniversidad Central de Venezuela, Facultad de CienciasA new numerical scheme for solving transient pressure in a confined aquifer is presented. It is based on the fundamental solution method (FSM) and it combines free Green functions, superposition principle, and singular value decomposition (SVD) method to obtain an efficient computational algorithm to approximate unsteady pressure in general two dimensional groundwater problems. Its mathematical formulation avoids integral equations, is meshfree, and its new multistep approach provides very accurate approximation of full transient aquifer pressure along any period of time. The new scheme was validated with synthetic aquifers problems with constant and variable well rates. Its applications to arbitrary shaped aquifer with multiple wells is developed and analyzed. Numerical results gave evidence that the new scheme is a versatile tool and an alternative choice to boundary element methods to solve groundwater problems. Keywords: multistep, meshless, fundamental solution method, free Green function, singular value decomposition.https://revistas.ucr.ac.cr/index.php/matematica/article/view/1423 |
| spellingShingle | Juan M. Guevara-Jordan Carmen M. Da Silva-Rodrigues A multistep fundamental solution scheme for modeling groundwater flow Revista de Matemática: Teoría y Aplicaciones |
| title | A multistep fundamental solution scheme for modeling groundwater flow |
| title_full | A multistep fundamental solution scheme for modeling groundwater flow |
| title_fullStr | A multistep fundamental solution scheme for modeling groundwater flow |
| title_full_unstemmed | A multistep fundamental solution scheme for modeling groundwater flow |
| title_short | A multistep fundamental solution scheme for modeling groundwater flow |
| title_sort | multistep fundamental solution scheme for modeling groundwater flow |
| url | https://revistas.ucr.ac.cr/index.php/matematica/article/view/1423 |
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