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

Analytical Solution for Solute Transport in Semi-Infinite Heterogeneous Porous Media

2011 ◽  
Vol 312-315 ◽  
pp. 495-499
Author(s):  
B.Q. Deng ◽  
Y.F. Qiu ◽  
C.N. Kim
Keyword(s):  
Porous Media ◽  
Analytical Solution ◽  
Solute Transport ◽  
Integral Transform ◽  
Integral Transforms ◽  
Heterogeneous Porous Media ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Integral Transform Technique ◽  
Linear Decay

Solute transport in porous media concerns advection, dispersion, sorption, and reaction. Since porous media is commonly heterogeneous, the properties of porous media are spatially and temporally variable. In this paper, one dimensional unsteady solute transport in semi-infinite heterogeneous porous media is investigated. Both linear and nonlinear decay is considered. Analytical solution is obtained for linear decay with spatially and temporally diffusion coefficient and velocity by using generalized integral transform technique. The inverse integral transforms are developed for the problems in semi-infinite space based on some weighted functions. Some examples are given to show the application of the method and analytical solutions.

scholarly journals A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Silvia Jerez ◽  
Ivan Dzib
Keyword(s):  
Numerical Simulation ◽  
Analytical Solution ◽  
Fractional Derivative ◽  
Dispersion Equation ◽  
Numerical Algorithm ◽  
Initial Condition ◽  
Discrete Method ◽  
One Dimensional ◽  
Advection Dispersion ◽  
The One

We obtain a numerical algorithm by using the space-time conservation element and solution element (CE-SE) method for the fractional advection-dispersion equation. The fractional derivative is defined by the Riemann-Liouville formula. We prove that the CE-SE approximation is conditionally stable under mild requirements. A numerical simulation is performed for the one-dimensional case by considering a benchmark with a discontinuous initial condition in order to compare the results with the analytical solution.

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.

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