Analytical Solutions for Advection and Advection-Diffusion Equations with Spatially Variable Coefficients

Zoppou, Christopher; Knight, J. H.

doi:10.1061/(asce)0733-9429(1997)123:2(144)

Cited by 102 publications

(64 citation statements)

References 7 publications

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“…In the works of Yates (1990), Logan (1996) and Zoppou and Knight (1997), the dispersion coefficient was also considered as spatially dependent but to go on increasing as x increases along the semi-infinite domain; hence its limiting value was assumed. In the present work, the changes due either to heterogeneity or to unsteadiness can be managed so as to remain small or of a desired order, by choosing appropriate values of their respective parameters, a and m. In addition, a function for the velocity may be interpolated to describe heterogeneity of decreasing order.…”

Section: Discussionmentioning

confidence: 99%

One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity

Kumar

Jaiswal

Kumar

2012

Hydrological Sciences Journal

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Section: Discussionmentioning

confidence: 99%

One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity

Kumar

Jaiswal

Kumar

2012

Hydrological Sciences Journal

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“…where boundaries are symmetrical the solution of the problem is given by the first term the equation (17). The second term is equation (17) is thus due to the asymmetric boundary imposed in the more general problem.…”

Section: Evaluation Of the Integral Solutionmentioning

confidence: 99%

Mathematical Analysis of Solute Transport Exponentially Varies With Time in Unsaturated Soil Media

Raji¹

2016

IJRET

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The wide range of contamination sources is one of many factors contributing to the complexity of groundwater quality assessment. Contaminants containing different chemicals will pass through different hydrologic zones as they migrate through the soil to the water table. Mathematical analysis is presented for simultaneous dispersion and adsorption of a solute within homogenous and isotropic porous media in steady unidirectional flow fields. The dispersion systems are adsorbing the solute at rates proportional to their concentration and are subject to input concentrations that vary exponentially with time. In this study, the advection-dispersion equation has been solved analytically to evaluate the transport of pollutants which takes into account of distribution coefficient and porosity by considering input concentrations of pollutants. The solution is obtained using Laplace transform, moving coordinates and Duhamel's theorem is used to get the solution in terms of complementary error function.Mathematical solutions are developed for predicting the concentration of contaminants in adsorbing porous media for prescribed media and fluid parameters.

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“…In the literature, the researchers have restricted themselves up to simple continuous Dirichlet BCs and moments derivation up to second order. Thus, our solutions are more general and we went few steps beyond all previous studies [25][26][27][28][29]. Moreover, it is important to mention that the Danckwerts type boundary conditions are more appropriate for the solution of current model equations which account for back mixing in the case of large axial dispersion [30].…”

Section: Introductionmentioning

confidence: 97%

Analysis of One-Dimensional Advection–Diffusion Model with Variable Coefficients Describing Solute Transport in a Porous medium

2017

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This work presents the analytical solution and temporal moments of one-dimensional advection-diffusion model with variable coefficients. Two case studies along with the two different sets of boundary conditions are considered at the inlet and outlet of the domain. In the first case, a time dependent solute dispersion in the homogeneous domain along uniform flow is taken into account, whereas in the second case, due to inhomogeneity of domain, velocity is taken spatially dependent and the dispersion is assumed proportional to the square of the velocity. The Laplace transform is used to obtain the analytical solutions. The analytical temporal moments are derived from the Laplace domain solutions. To verify the correctness of the analytical solutions, a high resolution second order finite volume scheme is applied. Different case studies are considered and discussed. Both analytical and numerical results are in good agreement with each other.Keywords Advection-diffusion equation · rectangular pulse injections · analytical solutions · moment analysis · finite volume method · dynamic simulations. Mathematics Subject Classification (2000) 80A23 · 26A33 · 42A16

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Analytical Solutions for Advection and Advection-Diffusion Equations with Spatially Variable Coefficients

Cited by 102 publications

References 7 publications

One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity

One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity

Mathematical Analysis of Solute Transport Exponentially Varies With Time in Unsaturated Soil Media

Analysis of One-Dimensional Advection–Diffusion Model with Variable Coefficients Describing Solute Transport in a Porous medium

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