Time-space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation

2018-05-01
Tu, Tongbi
Ercan, Ali
Kavvas, M. Levent
Show full item record
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
113
views
0
downloads
In order to model non-Fickian transport behaviour in groundwater aquifers, various forms of the time-space fractional advection-dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time-space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time-space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time-space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time-space fractional mass conservation equation and the time-space fractional water flux equation. Here, we apply these time-space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time-space. The numerical results demonstrate that the proposed time-space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy-tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long-range dependence of the underlying groundwater flow field.
Caputo fractional derivative, confined aquifer, groundwater flow, numerical solution, time-space fractional governing equation, NON-FICKIAN TRANSPORT, FINITE-DIFFERENCE APPROXIMATIONS, ADVECTION-DISPERSION EQUATION, ANOMALOUS DIFFUSION, MEDIA, DYNAMICS, MODELS
https://hdl.handle.net/11511/99972
HYDROLOGICAL PROCESSES
Department of Civil Engineering, Article

Suggestions

Performance Assessment of NAMI DANCE in Tsunami Evolution and Currents Using a Benchmark Problem
Velioglu, Deniz; Kian, Rozita; Yalçıner, Ahmet Cevdet; Zaytsev, Andrey (2016-09-01)
Numerical modeling of tsunami evolution, propagation, and inundation is complicated due to numerous parameters involved in the phenomenon. It is important to assess the performance of numerical codes that solve tsunami motion, as well as flow and velocity patterns. NAMI DANCE is a computational tool developed for the modeling of long waves. It provides numerical modeling and efficient visualization of tsunami generation, propagation, and inundation mechanisms and computes the tsunami parameters. In the theo...
Time-space fractional governing equations of one-dimensional unsteady open channel flow process: Numerical solution and exploration
Ercan, Ali; Kavvas, M. Levent (2017-07-01)
Although fractional integration and differentiation have found many applications in various fields of science, such as physics, finance, bioengineering, continuum mechanics, and hydrology, their engineering applications, especially in the field of fluid flow processes, are rather limited. In this study, a finite difference numerical approach is proposed to solve the time-space fractional governing equations of 1-dimensional unsteady/non-uniform open channel flow process. By numerical simulations, results of...
Numerical modeling of wave diffraction in one-dimensional shoreline change model
Baykal, Cüneyt; Ergin, Ayşen; Department of Civil Engineering (2006)
In this study, available coastal models are briefly discussed and under wind waves and a numerical shoreline change model for longshore sediment transport based on “one-line” theory is developed. In numerical model, wave diffraction phenomenon in one-dimensional modeling is extensively discussed and to represent the irregular wave diffraction in the sheltered zones of coastal structures a simpler approach based on the methodology introduced by Kamphuis (2000) is proposed. Furthermore, the numerical model re...
Numerical modeling of wind wave induced longshore sediment transport
Şafak, Ilgar; Ergin, Ayşen; Department of Civil Engineering (2006)
In this study, a numerical model is developed to determine shoreline changes due to wind wave induced longshore sediment transport, by solving sediment continuity equation and taking one line theory as a base, in existence of seawalls, groins, T-groins, offshore breakwaters and beach nourishment projects, whose dimensions and locations may be given arbitrarily. The model computes the transformation of deep water wave characteristics up to the surf zone and eventually gives the result of shoreline changes wi...
Hydrodynamic Modeling of Dam-Reservoir Response during Earthquakes
Aydın, İsmail (American Society of Civil Engineers (ASCE), 2011-08-03)
A computational model is developed to analyze the hydrodynamic behavior of dam reservoirs during earthquakes. The mathematical model is based on the solution of two-dimensional (2D) Navier-Stokes equations in a vertical, semi-infinite domain truncated by a far-end boundary condition. A depth integrated continuity equation is used to track the deforming free-surface and ensure global mass conservation. A combination of Sommerfeld nonreflecting boundary and dissipation zone methods is implemented at the far e...
Citation Formats
T. Tu, A. Ercan, and M. L. Kavvas, “Time-space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation,” HYDROLOGICAL PROCESSES, vol. 32, no. 10, pp. 1406–1419, 2018, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/99972.
METU IIS - Integrated Information Service open@metu.edu.tr