Reply [to “Comment on ‘Analytical solutions of the nonlinear groundwater flow equation in unconfined aquifers and the effect of heterogeneity’ by Sergio E. Serrano”]

1999 ◽  
Vol 35 (1) ◽  
pp. 345-346
Author(s):  
Sergio E. Serrano
Keyword(s):  
Groundwater Flow ◽  
Analytical Solutions ◽  
Flow Equation ◽  
Unconfined Aquifers ◽  
Groundwater Flow Equation

A possible modification of groundwater flow equation using coordinate transformations

2014 ◽  
Vol 15 (2) ◽  
pp. 278-287 ◽  
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.

scholarly journals Groundwater flow equation, overview, derivation, and solution

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.

scholarly journals New groundwater flow equation with its exact solution

2016 ◽  
Vol 23 (4) ◽  
pp. 1837-1843 ◽  
Author(s):  
Abdon Atangana ◽  
Canan Ünlü
Keyword(s):  
Exact Solution ◽  
Groundwater Flow ◽  
Flow Equation ◽  
Groundwater Flow Equation
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