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 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 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 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 Governing equations of transient soil water flow and soil water flux in multi – dimensional fractional anisotropic media and fractional time

2016 ◽  
Author(s):  
M. Levent Kavvas ◽  
Ali Ercan ◽  
James Polsinelli
Keyword(s):  
Fractional Derivative ◽  
Soil Water ◽  
Water Flow ◽  
Continuity Equation ◽  
Water Flux ◽  
Anisotropic Media ◽  
Governing Equations ◽  
Soil Matrix ◽  
Soil Water Flow ◽  
Soil Water Flux

Abstract. In this study dimensionally-consistent governing equations of continuity and motion for transient soil water flow and soil water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. Due to the anisotropy in the hydraulic conductivities of natural soils, the soil medium within which the soil water flow occurs is essentially anisotropic. Accordingly, in this study the fractional dimensions in two horizontal and one vertical directions are considered to be different, resulting in multi-fractional multi-dimensional soil space within which the flow takes place. Toward the development of the fractional governing equations, first a dimensionally-consistent continuity equation for soil water flow in multi-dimensional fractional soil space and fractional time is developed. It is shown that the fractional soil water flow continuity equation approaches the conventional integer form of the continuity equation as the fractional derivative powers approach integer values. For the motion equation of soil water flow, or the equation of water flux within the soil matrix in multi-dimensional fractional soil space and fractional time, a dimensionally consistent equation is also developed. Again, it is shown that this fractional water flux equation approaches the conventional Darcy's equation as the fractional derivative powers approach integer values. From the combination of the fractional continuity and motion equations, the governing equation of transient soil water flow in multi-dimensional fractional soil space and fractional time is obtained. It is shown that this equation approaches the conventional Richards equation as the fractional derivative powers approach integer values. Then by the introduction of the Brooks-Corey constitutive relationships for soil water into the fractional transient soil water flow equation, an explicit form of the equation is obtained in multi-dimensional fractional soil space and fractional time. The governing fractional equation is then specialized to the case of only vertical soil water flow and of only horizontal soil water flow in fractional time-space. It is shown that the developed governing equations, in their fractional time but integer space forms, show behavior consistent with the previous experimental observations concerning the diffusive behavior of soil water flow.

scholarly journals Governing equations of transient soil water flow and soil water flux in multi-dimensional fractional anisotropic media and fractional time

2017 ◽  
Vol 21 (3) ◽  
pp. 1547-1557 ◽  
Author(s):  
M. Levent Kavvas ◽  
Ali Ercan ◽  
James Polsinelli
Keyword(s):  
Fractional Derivative ◽  
Soil Water ◽  
Water Flow ◽  
Continuity Equation ◽  
Water Flux ◽  
Anisotropic Media ◽  
Governing Equations ◽  
Soil Matrix ◽  
Soil Water Flow ◽  
Soil Water Flux

Abstract. In this study dimensionally consistent governing equations of continuity and motion for transient soil water flow and soil water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. Due to the anisotropy in the hydraulic conductivities of natural soils, the soil medium within which the soil water flow occurs is essentially anisotropic. Accordingly, in this study the fractional dimensions in two horizontal and one vertical directions are considered to be different, resulting in multi-fractional multi-dimensional soil space within which the flow takes place. Toward the development of the fractional governing equations, first a dimensionally consistent continuity equation for soil water flow in multi-dimensional fractional soil space and fractional time is developed. It is shown that the fractional soil water flow continuity equation approaches the conventional integer form of the continuity equation as the fractional derivative powers approach integer values. For the motion equation of soil water flow, or the equation of water flux within the soil matrix in multi-dimensional fractional soil space and fractional time, a dimensionally consistent equation is also developed. Again, it is shown that this fractional water flux equation approaches the conventional Darcy equation as the fractional derivative powers approach integer values. From the combination of the fractional continuity and motion equations, the governing equation of transient soil water flow in multi-dimensional fractional soil space and fractional time is obtained. It is shown that this equation approaches the conventional Richards equation as the fractional derivative powers approach integer values. Then by the introduction of the Brooks–Corey constitutive relationships for soil water into the fractional transient soil water flow equation, an explicit form of the equation is obtained in multi-dimensional fractional soil space and fractional time. The governing fractional equation is then specialized to the case of only vertical soil water flow and of only horizontal soil water flow in fractional time–space. It is shown that the developed governing equations, in their fractional time but integer space forms, show behavior consistent with the previous experimental observations concerning the diffusive behavior of soil water flow.

scholarly journals Remarks on the hydrogeological setting of S. Eufemia Lamezia plain through the development of the top surface of the intermediate confined aquifer (central Calabria)

2015 ◽  
Vol 4 (3) ◽  
Author(s):  
Enzo Cuiuli
Keyword(s):  
Groundwater Flow ◽  
Shallow Aquifer ◽  
Direct Transfer ◽  
Confined Aquifer ◽  
Geological Data ◽  
Recharge Rate ◽  
Hydrogeological Setting ◽  
Artesian Aquifer ◽  
Rainfall Recharge ◽  
Clay Horizon

The S. Eufemia Lamezia plain, located in central Calabria, is characterized by the presence of a multi-layered aquifer. In particular, it was studied the intermediate artesian aquifer, content in the Pliocene sands and sandstones. The collection of new lithostratigraphic data, related to drilling for water supplies, allowed to draw the map of the top of intermediate artesian aquifer underlying in the study area. The top surface of sands and sandstones map, presented here, seems to confirm the structural-geological data of the surface showing, also in depth, the conditioning of tectonics on the study area and on the groundwater flow. The analysis of the selected stratigraphic data shows that the studied aquifer is constituted by Pliocene deposits of sand and sandstones, confined to the top by Pliocene clay. Therefore locally hydraulic connections with the shallow aquifer for leackage phenomena are possible. The supply of the studied aquifer happens mainly for lateral recharge because the clay horizon that borders with the top of the aquifer prevents direct transfer of rainfall recharge. However, a reduced recharge rate is due to the meteoric recharge, which is possible in limited parts of the territory to the east of the study area and over. Therefore, this study aims to implement the knowledge of the groundwater flow of S. Eufemia plain by returning the top intermediate confined aquifer map which, is little studied but strongly exploited because, respect to the shallow aquifer, is more productive and more protected by potential contamination due to the presence of the aquiclude/aquitard which isolates it by the top.

scholarly journals Numerical Simulation of Micromixing of Particles and Fluids with Galloping Cylinder

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 580 ◽  
Author(s):  
Zahra Abdelmalek ◽  
Mohammad Yaghoub Abdollahzadeh Jamalabadi
Keyword(s):  
Continuity Equation ◽  
Stokes Equations ◽  
The Self ◽  
Moving Mesh ◽  
Navier Stokes ◽  
Parameter Study ◽  
Mems Devices ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Moving Cylinder

Micromixers are significant segments inside miniaturized scale biomedical frameworks. Numerical investigation of the effects of galloping cylinder characteristics inside a microchannel Newtonian, incompressible fluid in nonstationary condition is performed. Governing equations of the system include the continuity equation, and Navier–Stokes equations are solved within a moving mesh domain. The symmetry of laminar entering the channel is broken by the self-sustained motion of the cylinder. A parameter study on the amplitude and frequency of passive moving cylinder on the mixing of tiny particles in the fluid is performed. The results show a significant increase to the index of mixing uses of the galloping body in biomedical frameworks in the course of micro-electromechanical systems (MEMS) devices.

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