Abstract
One dimensional advection dispersion equation is analytically solved initially in solute free domain by considering uniform exponential decay input condition at origin. Heterogeneous medium of semi infinite extent is considered. Due to heterogeneity velocity and dispersivity coefficient of the advection dispersion equation are considered functions of space variable and time variable. Analytical solution is obtained using Laplace transform technique when dispersivity depended on velocity. The effects of first order decay term and adsorption are studied. The graphical representations are made using MATLAB
Highlights
Managing the groundwater resources and rehabilitation of polluted aquifers, mathematical modeling is a powerful tool
Analytical solutions in one, two, and three-dimensional advection-dispersion transport equations with constant coefficients in homogeneous medium which have been collected in various compendiums [1,2,3,4]
Using the theory [11] that relates dispersion directly to velocity, analytical solutions were obtained for solute transport along unsteady flow through homogeneous medium [12,13,14,15]
Summary
Managing the groundwater resources and rehabilitation of polluted aquifers, mathematical modeling is a powerful tool. Analytical solutions in one-, two-, and three-dimensional advection-dispersion transport equations with constant coefficients in homogeneous medium which have been collected in various compendiums [1,2,3,4]. Using the theory [11] that relates dispersion directly to velocity, analytical solutions were obtained for solute transport along unsteady flow through homogeneous medium [12,13,14,15]. Analytical solutions for heterogeneous porous media for transport equation with time dependent coefficients [20,21,22,23]. Further the technique of generalized integral transform to get analytical solutions of ADE in heterogeneous media with different spatially dependent dispersivity discussed [29]. In the present work one-dimensional advection diffusion equation is solved for dispersivity depended on square of velocity. Laplace transform technique is used to obtain the analytical solution
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