IMPROVEMENT OF THE ANALYTICAL SOLUTION OF THE ADVECTION- DISPERSION EQUATION FOR USE IN INVERSE TASKS.

2018 ◽  
Author(s):  
Marek Sokac
Keyword(s):  
Analytical Solution ◽  
Dispersion Equation ◽  
Advection Dispersion

scholarly journals Analytical Solution of 1D Advection-Dispersion Equation In Finite Groundwater Reservoir With Spatially Dependent Dispersivity And Two Inputs Sources With Source-Sink Term Impact

2021 ◽  
Author(s):  
Thomas TJOCK-MBAGA ◽  
Patrice Ele Abiama ◽  
Jean Marie Ema'a Ema'a ◽  
Germain Hubert Ben-Bolie
Keyword(s):  
Analytical Solution ◽  
Linear Function ◽  
Dispersion Equation ◽  
Source Term ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Liouville Problem ◽  
Finite Domain ◽  
Advection Dispersion ◽  
Sink Term

Abstract This study derives an analytical solution of a one-dimensional (1D) advection-dispersion equation (ADE) for solute transport with two contaminant sources that takes into account the source term. For a heterogeneous medium, groundwater velocity is considered as a linear function while the dispersion as a nth-power of linear function of space and analytical solutions are obtained for and . The solution in a heterogeneous finite domain with unsteady coefficients is obtained using the Generalized Integral Transform Technique (GITT) with a new regular Sturm-Liouville Problem (SLP). The solutions are validated with the numerical solutions obtained using MATLAB pedpe solver and the existing solution from the proposed solutions. We exanimated the influence of the source term, the heterogeneity parameters and the unsteady coefficient on the solute concentration distribution. The results show that the source term produces a solute build-up while the heterogeneity level decreases the concentration level in the medium. As an illustration, model predictions are used to estimate the time histories of the radiological doses of uranium at different distances from the sources boundary in order to understand the potential radiological impact on the general public.

Analytical Solution of Advection-Dispersion Equation with Spatially Dependent Dispersivity

2017 ◽  
Vol 143 (11) ◽  
pp. 04017126 ◽  
Author(s):  
Vinod Kumar Bharati ◽  
Vijay P. Singh ◽  
Abhishek Sanskrityayn ◽  
Naveen Kumar
Keyword(s):  
Analytical Solution ◽  
Dispersion Equation ◽  
Advection Dispersion

ONE-DIMENSIONAL TEMPORALLY DEPENDENT ADVECTION-DISPERSION EQUATION IN POROUS MEDIA: ANALYTICAL SOLUTION

2010 ◽  
Vol 23 (4) ◽  
pp. 521-539 ◽  
Author(s):  
R. R. YADAV ◽  
DILIP KUMAR JAISWAL ◽  
HAREESH KUMAR YADAV ◽  
GUL RANA
Keyword(s):  
Porous Media ◽  
Analytical Solution ◽  
Dispersion Equation ◽  
One Dimensional ◽  
Advection Dispersion

scholarly journals Numerical routing of tracer concentrations in rivers with stagnant zones

2016 ◽  
Vol 17 (3) ◽  
pp. 825-834 ◽  
Author(s):  
Abbas Parsaie ◽  
Amir Hamzeh Haghiabi
Keyword(s):  
Numerical Model ◽  
Analytical Solution ◽  
Dispersion Equation ◽  
Splitting Technique ◽  
Advection Dispersion ◽  
The Uk ◽  
Engineering Modeling ◽  
Pollution Transmission ◽  
Good Agreement ◽  
Numerical Approaches

Modeling pollution transmission in rivers is an important subject in environmental engineering studies. Numerical approaches to modeling pollution transmission in rivers are useful tools for managing the water quality. The advection-dispersion equation is the governing equation in the transport of pollution in rivers. Recently, due to advances in fractional calculus in engineering modeling, the simulation of pollution transmission in rivers has been improved using the fractional derivative approach. In this study, by solving the fractional advection-dispersion equation (FRADE), a numerical model was developed for the simulation of pollution transmission in rivers with stagnant zones. To this purpose, both terms of the FRADE equation (advection and fractional dispersion) were discretized separately and the results were connected using a time-splitting technique. The analytical solution of a modified advection-dispersion equation (MADE) model and observed data from the Severn River in the UK were used to demonstrate the model capabilities. Results indicated that there is a good agreement between observed data, the analytical solution of the MADE model, and the results of the developed numerical model. The developed numerical model can accurately simulate the long-tailed dispersion processes in a natural river.

scholarly journals An Analytical Solution of the Advection Dispersion Equation in a Bounded Domain and Its Application to Laboratory Experiments

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
M. Massabó ◽  
R. Cianci ◽  
O. Paladino
Keyword(s):  
Porous Medium ◽  
Analytical Solution ◽  
Dispersion Equation ◽  
Saturated Porous Medium ◽  
Infinite Domain ◽  
Noninvasive Technique ◽  
Advection Dispersion ◽  
Experimental Apparatus ◽  
Plate Geometry ◽  
Mixed Types

We study a uniform flow in a parallel plate geometry to model contaminant transport through a saturated porous medium in a semi-infinite domain in order to simulate an experimental apparatus mainly constituted by a chamber filled with a glass beads bed. The general solution of the advection dispersion equation in a porous medium was obtained by utilizing the Jacobiθ3Function. The analytical solution here presented has been provided when the inlet (Dirac) and the boundary conditions (Dirichelet, Neumann, and mixed types) are fixed. The proposed solution was used to study experimental data acquired by using a noninvasive technique.

Analytical Solution for Advection-Dispersion Equation of the Pollutant Concentration using Laplace Transformation

2021 ◽  
Vol 4 (1) ◽  
pp. 33-40
Author(s):  
Keshav Paudel ◽  
Prem Sagar Bhandari ◽  
Jeevan Kafle
Keyword(s):  
Analytical Solution ◽  
Dispersion Equation ◽  
Laplace Transformation ◽  
Dispersion Coefficient ◽  
Oxygen Demand ◽  
Pollutant Concentration ◽  
One Dimension ◽  
Advection Dispersion ◽  
State Case ◽  
Saturated Oxygen

We present simple analytical solution for the unsteady advection-dispersion equation describing the pollutant concentration C(x; t) in one dimension. In this model the water velocity in the x-direction is taken as a linear function of x and dispersion coefficient D as zero. In this paper by taking k = 0, k is the half saturated oxygen demand concentration for pollutant decay, we can apply the Laplace transformation and obtain the solution. The variation of C(x; t) with different times t upto t → ∞ (the steady state case) is taken into account advection-dispersion equation in our study.

scholarly journals Approximate Analytical Solution of Advection-Dispersion Equation By Means of OHAM.

2018 ◽  
Vol 7 (1) ◽  
pp. 15-20
Author(s):  
D J Prajapati ◽  
N B Desai
Keyword(s):  
Analytical Solution ◽  
Dispersion Equation ◽  
Graphical Representation ◽  
Approximate Analytical Solution ◽  
Time Dependent ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Advection Dispersion ◽  
Homotopy Analysis ◽  
Input Source

This work deals with the analytical solution of advection dispersion equation arising in solute transport along unsteady groundwater flow in finite aquifer. A time dependent input source concentration is considered at the origin of the aquifer and it is assumed that the concentration gradient is zero at the other end of the aquifer. The optimal homotopy analysis method (OHAM) is used to obtain numerical and graphical representation.

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