scholarly journals The Use of Fractional Order Derivative to Predict the Groundwater Flow

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Abdon Atangana ◽  
Necdet Bildik
Keyword(s):  
Analytical Solution ◽  
Groundwater Flow ◽  
Discharge Rate ◽  
Test Site ◽  
Pumping Test ◽  
Flow Equation ◽  
Perfect Agreement ◽  
Transform Method ◽  
Groundwater Flow Equation ◽  
The University

The aim of this work was to convert the Thiem and the Theis groundwater flow equation to the time-fractional groundwater flow model. We first derived the analytical solution of the Theim time-fractional groundwater flow equation in terms of the generalized Wright function. We presented some properties of the Laplace-Carson transform. We derived the analytical solution of the Theis-time-fractional groundwater flow equation (TFGFE) via the Laplace-Carson transform method. We introduced the generalized exponential integral, as solution of the TFGFE. This solution is in perfect agreement with the data observed from the pumping test performed by the Institute for Groundwater Study on one of its borehole settled on the test site of the University of the Free State. The test consisted of the pumping of the borehole at the constant discharge rateQand monitoring the piezometric head for 350 minutes.

scholarly journals Analytical Solutions of a Space-Time Fractional Derivative of Groundwater Flow Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Abdon Atangana ◽  
P. D. Vermeulen
Keyword(s):  
Groundwater Flow ◽  
Numerical Solutions ◽  
Discharge Rate ◽  
Adomian Decomposition Method ◽  
Flow Equation ◽  
Darcy Law ◽  
Perfect Agreement ◽  
Piezometric Head ◽  
Adomian Decomposition ◽  
Groundwater Flow Equation

The classical Darcy law is generalized by regarding the water flow as a function of a noninteger order derivative of the piezometric head. This generalized law and the law of conservation of mass are then used to derive a new equation for groundwater flow. Two methods including Frobenius and Adomian decomposition method are used to obtain an asymptotic analytical solution to the generalized groundwater flow equation. The solution obtained via Frobenius method is valid in the vicinity of the borehole. This solution is in perfect agreement with the data observed from the pumping test performed by the institute for groundwater study on one of their boreholes settled on the test site of the University of the Free State. The test consisted of the pumping of the borehole at the constant discharge rateQand monitoring the piezometric head for 350 minutes. Numerical solutions obtained via Adomian method are compared with the Barker generalized radial flow model for which a fractal dimension for the flow is assumed. Proposition for uncertainties in groundwater studies was given.

A Simple Analytical Solution for the Boussinesq One-Dimensional Groundwater Flow Equation

1984 ◽  
Vol 20 (1) ◽  
pp. 24-28 ◽  
Author(s):  
Panagiotis K. Tolikas ◽  
Epaminondas G. Sidiropoulos ◽  
Christos D. Tzimopoulos
Keyword(s):  
Analytical Solution ◽  
Groundwater Flow ◽  
Flow Equation ◽  
One Dimensional ◽  
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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