Modeling an Aquifer: Numerical Solution to the Groundwater Flow Equation

We present a model of groundwater dynamics under stationary flow and, governed by Darcy’s law of water motion through porous media, we apply it to study a 2D aquifer with water table of constant slope comprised of a homogeneous and isotropic media; the more realistic case of an homogeneous anisotropic soil is also considered. Taking into account some geophysical parameters we develop a computational routine, in the Finite Difference Method, which solves the resulting elliptic partial equation, both in a homogeneous isotropic and in a homogeneous anisotropic media. After calibration of the numerical model, this routine is used to begin a study of the Ayamonte-Huelva aquifer in Spain, a modest analysis of the system is given, and we compute the average discharge vector as well as its root mean square as a first predictive approximation of the flux in this system, providing us a signal of the location of best exploitation; long term goal is to develop a complete computational tool for the analysis of groundwater dynamics.

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A possible modification of groundwater flow equation using coordinate transformations

Water Science & Technology Water Supply ◽

10.2166/ws.2014.110 ◽

2014 ◽

Vol 15 (2) ◽

pp. 278-287 ◽

Cited By ~ 1

Author(s):

Abdon Atangana ◽

Ernestine Alabaraoye

Keyword(s):

Groundwater Flow ◽

Prolate Spheroid ◽

Flow Equation ◽

Time Space ◽

Adomian Decomposition ◽

Iteration Methods ◽

Groundwater Flow Equation ◽

Factor Α ◽

Modified Equation ◽

Good Agreement

We described a groundwater model with prolate spheroid coordinates, and introduced a new parameter, namely τ the silhouette influence of the geometric under which the water flows. At first, we supposed that the silhouette influence approaches zero; under this assumption, the modified equation collapsed to the ordinary groundwater flow equation. We proposed an analytical solution to the standard version of groundwater as a function of time, space and uncertainty factor α. Our proposed solution was in good agreement with experimental data. We presented a good approximation to the exponential integral. We obtained an asymptotic special solution to the modified equation by means of the Adomian decomposition and variational iteration methods.

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What can we learn from long-term groundwater data to improve climate change impact studies?

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-8-7621-2011 ◽

2011 ◽

Vol 8 (4) ◽

pp. 7621-7655 ◽

Cited By ~ 1

Author(s):

S. Stoll ◽

H. J. Hendricks Franssen ◽

R. Barthel ◽

W. Kinzelbach

Keyword(s):

Climate Change ◽

Land Use ◽

Climate Change Impact ◽

Large Scale ◽

Climate Models ◽

Groundwater Resources ◽

Groundwater Dynamics ◽

Impact Studies ◽

Change Impact

Abstract. Future risks for groundwater resources, due to global change are usually analyzed by driving hydrological models with the outputs of climate models. However, this model chain is subject to considerable uncertainties. Given the high uncertainties it is essential to identify the processes governing the groundwater dynamics, as these processes are likely to affect groundwater resources in the future, too. Information about the dominant mechanisms can be achieved by the analysis of long-term data, which are assumed to provide insight in the reaction of groundwater resources to changing conditions (weather, land use, water demand). Referring to this, a dataset of 30 long-term time series of precipitation dominated groundwater systems in northern Switzerland and southern Germany is collected. In order to receive additional information the analysis of the data is carried out together with hydrological model simulations. High spatio-temporal correlations, even over large distances could be detected and are assumed to be related to large-scale atmospheric circulation patterns. As a result it is suggested to prefer innovative weather-type-based downscaling methods to other stochastic downscaling approaches. In addition, with the help of a qualitative procedure to distinguish between meteorological and anthropogenic causes it was possible to identify processes which dominated the groundwater dynamics in the past. It could be shown that besides the meteorological conditions, land use changes, pumping activity and feedback mechanisms governed the groundwater dynamics. Based on these findings, recommendations to improve climate change impact studies are suggested.

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Application of the Lanczos Algorithm to the solution of the groundwater flow equation

Water Resources Research ◽

10.1029/wr025i003p00551 ◽

1989 ◽

Vol 25 (3) ◽

pp. 551-558 ◽

Cited By ~ 20

Author(s):

W. Scott Dunbar ◽

Allan D. Woodbury

Keyword(s):

Groundwater Flow ◽

Flow Equation ◽

Lanczos Algorithm ◽

Groundwater Flow Equation

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Groundwater flow equation, overview, derivation, and solution

E3S Web of Conferences ◽

10.1051/e3sconf/202131404007 ◽

2021 ◽

Vol 314 ◽

pp. 04007

Author(s):

Lhoussaine El Mezouary ◽

Bouabid El Mansouri

Keyword(s):

Heat Transfer ◽

Differential Equation ◽

Groundwater Flow ◽

Numerical Solutions ◽

Flow Equation ◽

Heat Transfer Equation ◽

Flow Equations ◽

Basic Law ◽

Flow Through ◽

Groundwater Flow Equation

Darcy’s law is the basic law of flow, and it produces a partial differential equation is similar to the heat transfer equation when coupled with an equation of continuity that explains the conservation of fluid mass during flow through a porous media. This article, titled the groundwater flow equation, covers the derivation of the groundwater flow equations in both the steady and transient states. We look at some of the most common approaches and methods for developing analytical or numerical solutions. The flaws and limits of these solutions in reproducing the behavior of water flow on the aquifer are also discussed in the article.

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