scholarly journals Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time

2019 ◽  
Author(s):  
M. Levent Kavvas ◽  
Tongbi Tu ◽  
Ali Ercan ◽  
James Polsinelli
Keyword(s):  
Groundwater Flow ◽  
Governing Equation ◽  
Water Flux ◽  
Unconfined Aquifer ◽  
Saturated Porous Media ◽  
Numerical Application ◽  
Unconfined Aquifers ◽  
Consistent Equation ◽  
Fractional Dimensions ◽  
Fractional Space

Abstract. In this study, a dimensionally-consistent governing equation of transient unconfined groundwater flow in fractional time and multi-fractional space is developed. First, a fractional continuity equation for transient unconfined groundwater flow is developed in fractional time and space. For the equation of groundwater motion within a multi-fractional multi-dimensional unconfined aquifer, a previously-developed dimensionally consistent equation for water flux in unsaturated/saturated porous media is combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. Combining the fractional continuity and groundwater motion equations, the fractional governing equation of transient unconfined aquifer flow is then obtained. Finally, a numerical application to an unconfined aquifer groundwater flow problem is presented to show the skills of the proposed fractional governing equation.

scholarly journals Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time

2020 ◽  
Vol 11 (1) ◽  
pp. 1-12 ◽  
Author(s):  
M. Levent Kavvas ◽  
Tongbi Tu ◽  
Ali Ercan ◽  
James Polsinelli
Keyword(s):  
Groundwater Flow ◽  
Governing Equation ◽  
Water Flux ◽  
Unconfined Aquifer ◽  
Saturated Porous Media ◽  
Unconfined Aquifers ◽  
Heavy Tailed ◽  
Consistent Equation ◽  
Fractional Dimensions ◽  
Fractional Space

Abstract. In this study, a dimensionally consistent governing equation of transient unconfined groundwater flow in fractional time and multi-fractional space is developed. First, a fractional continuity equation for transient unconfined groundwater flow is developed in fractional time and space. For the equation of groundwater motion within a multi-fractional multidimensional unconfined aquifer, a previously developed dimensionally consistent equation for water flux in unsaturated/saturated porous media is combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. Combining the fractional continuity and groundwater motion equations, the fractional governing equation of transient unconfined aquifer flow is then obtained. Finally, two numerical applications to unconfined aquifer groundwater flow are presented to show the skills of the proposed fractional governing equation. As shown in one of the numerical applications, the newly developed governing equation can produce heavy-tailed recession behavior in unconfined aquifer discharges.

scholarly journals Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time

2017 ◽  
Vol 8 (4) ◽  
pp. 921-929 ◽  
Author(s):  
M. Levent Kavvas ◽  
Tongbi Tu ◽  
Ali Ercan ◽  
James Polsinelli
Keyword(s):  
Groundwater Flow ◽  
Governing Equation ◽  
Continuity Equation ◽  
Flow Problem ◽  
Water Flux ◽  
Confined Aquifer ◽  
Governing Equations ◽  
Numerical Application ◽  
Consistent Equation ◽  
Fractional Dimensions

Abstract. Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally consistent equation is also developed. The governing equation of transient saturated groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained by combining the fractional continuity and water flux equations. To illustrate the capability of the proposed governing equation of groundwater flow in a confined aquifer, a numerical application of the fractional governing equation to a confined aquifer groundwater flow problem was also performed.

scholarly journals Fractional Governing Equations of Transient Groundwater Flow in Confined Aquifers with Multi-Fractional Dimensions in Fractional Time

2017 ◽  
Author(s):  
M. Levent Kavvas ◽  
Tongbi Tu ◽  
Ali Ercan ◽  
James Polsinelli
Keyword(s):  
Groundwater Flow ◽  
Governing Equation ◽  
Continuity Equation ◽  
Water Flux ◽  
Confined Aquifer ◽  
Governing Equations ◽  
Confined Aquifers ◽  
Fractional Dimensions

Abstract. A dimensionally-consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a continuity equation for transient groundwater flow in fractional time and in a multi-fractional, multi-dimensional confined aquifer is developed. An equation of water flux is also developed. The governing equation of transient groundwater flow in a multi-fractional, multi-dimensional confined aquifer in fractional time is then obtained by combining the fractional continuity and water flux equations.

scholarly journals Numerical modeling of groundwater flow based on explicit and fully implicit schemes of finite volume method

2021 ◽  
Vol 9 (4B) ◽  
Author(s):  
Hüseyin Y. DALKILIÇ ◽  
◽  
Amin GHAREHBAGHI ◽  
Keyword(s):  
Groundwater Flow ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Water Table ◽  
Governing Equation ◽  
Unconfined Aquifer ◽  
Simulation Process ◽  
Water Table Fluctuations ◽  
Fully Implicit ◽  
Volume Method

This paper documents a novel numerical model for calculating the behavior of unsteady, one-dimensional groundwater flow by using the finite volume method. The developed model determined water table fluctuations for different scenarios as follows: Drainage and recession from an unconfined aquifer, and water table fluctuations above an inclined leaky layer due to ditch recharge with a constant and variable upper boundary condition. The Boussinesq equation, which is the governing equation in this domain, is linearized and solved numerically in both of the explicit and fully implicit conditions. Meanwhile, the upwind scheme is employed to discretize the governing equation. The computed outcomes of both the explicit and implicit approaches agreed well with the results of analytical solution and laboratory experiments. The main reason is that in the first half of simulation process explicit scheme obtains slightly better results and in the second half of the simulation process fully implicit scheme predicts more reliable outcomes that are hidden in the neighbor node points. As a final point, the numerical outcomes confirm that the developed model is capable of calculating satisfactory outcomes in engineering and science applications.

scholarly journals Groundwater flow to a horizontal or slanted well in an unconfined aquifer

2002 ◽  
Vol 38 (7) ◽  
pp. 13-1-13-11 ◽  
Author(s):  
Hongbin Zhan ◽  
Vitaly A. Zlotnik
Keyword(s):  
Groundwater Flow ◽  
Unconfined Aquifer

scholarly journals Hydrogeological Conceptual Model in the Middle of Randublatung Groundwater Basin

2021 ◽  
Vol 926 (1) ◽  
pp. 012078
Author(s):  
D L Setyaningsih ◽  
K D Setyawan ◽  
D P E Putra ◽  
Salahuddin
Keyword(s):  
Groundwater Flow ◽  
Conceptual Model ◽  
Unconfined Aquifer ◽  
Primary Data ◽  
Essential Information ◽  
Aquifer System ◽  
The North ◽  
Shallow Wells ◽  
Groundwater Basin ◽  
Constant Head

Abstract Randublatung groundwater basin is one of the groundwaters basins with massive utilization of groundwater pumping. However, the knowledge of the comprehensive hydrogeological system in this groundwater basin is limited, so this research aims to determine a comprehensive hydrogeological conceptual model of the Randublatung groundwater basin. The methodology was conducted by collecting secondary and primary data of deep and shallow wells to evaluate boundaries of pattern and direction of groundwater flow and develop the aquifer system’s geometry. The result shows that the groundwater flow boundaries are Grogol River in the west, Wado River in the East, Bengawan Solo river in the South as a river boundary, and Rembang Mountains in the North as a constant head boundary. Therefore, groundwater flows from the hills area to the Bengawan Solo River and the north as the river’s flow. Based on the log bor evaluation, the aquifer system of the study area consist of an unconfined aquifer with a maximum thickness of 20 m and three layers of confined aquifers with thickness vary between 8 to 60 m. the hydraulic conductivity of the aquifers depends on the aquifer’s lithology range from sand, gravel, limestone, and sandstone. This hydrogeological conceptual model provides essential information for numerical groundwater models in the middle of the Randublatung groundwater basin.

scholarly journals A new model of groundwater flow within an unconfined aquifer: Application of Caputo-Fabrizio fractional derivative

2019 ◽  
Vol 24 (7) ◽  
pp. 3227-3247 ◽  
Author(s):  
Pierre Aime Feulefack ◽  
◽  
Jean Daniel Djida ◽  
Atangana Abdon ◽  
Keyword(s):  
Fractional Derivative ◽  
Groundwater Flow ◽  
Unconfined Aquifer ◽  
New Model

Vadose Zone, Part I : Characterization and Flow Processes

2003 ◽  
Author(s):  
Yoram Rubin
Keyword(s):  
Porous Media ◽  
Water Flow ◽  
Governing Equation ◽  
Vadose Zone ◽  
Stochastic Analysis ◽  
Transport Processes ◽  
Richards Equation ◽  
Saturated Porous Media ◽  
Flow And Transport ◽  
Flow Processes

Many of the principles guiding stochastic analysis of flow and transport processes in the vadose zone are those which we also employ in the saturated zone, and which we have explored in earlier chapters. However, there are important considerations and simplifications to be made, given the nature of the flow and of the governing equations, which we explore here and in chapter 12. The governing equation for water flow in variably saturated porous media at the smallest scale where Darcy’s law is applicable (i.e., no need for upscaling of parameters) is Richards’ equation (cf. Yeh, 1998)

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