According to hydrology, water flowing in an aquifer follows the three-dimensional partial differential parabolic equation [see e.g. D. K. Todd: Groundwater Hydrology, Wiley and Sons, p.100 and p. 123].For a vertical well in an aquifer, often isotropy can be assumed, so that all conductivities are equal to a unique value K.Digital fields computed by equations (1), (3) often appear instable due to the parabolic nature of equation. Therefore it may be useful to compare digital fields to more precise analytical solutions.Solutions are obtained by assuming a product of two functions: one depending only on time and the other one depending only on the variable u containing time and distance r.
Analytical solutions of partial differential equations ina homogeneous and isotropic two-dimensional aquifer / Menziani, Marilena; Pugnaghi, Sergio; Santangelo, Renato; S., Vincenzi. - In: GEOPHYSICAL RESEARCH ABSTRACTS. - ISSN 1607-7962. - ELETTRONICO. - 7:(2005), pp. 03397-03397. (Intervento presentato al convegno 2nd European Geosciences Union General Assembly tenutosi a Vienna nel 24-29 March 2005).
Analytical solutions of partial differential equations ina homogeneous and isotropic two-dimensional aquifer
MENZIANI, Marilena;PUGNAGHI, Sergio;SANTANGELO, Renato;
2005
Abstract
According to hydrology, water flowing in an aquifer follows the three-dimensional partial differential parabolic equation [see e.g. D. K. Todd: Groundwater Hydrology, Wiley and Sons, p.100 and p. 123].For a vertical well in an aquifer, often isotropy can be assumed, so that all conductivities are equal to a unique value K.Digital fields computed by equations (1), (3) often appear instable due to the parabolic nature of equation. Therefore it may be useful to compare digital fields to more precise analytical solutions.Solutions are obtained by assuming a product of two functions: one depending only on time and the other one depending only on the variable u containing time and distance r.
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