Dispersion in Anisotropic, Homogeneous, Porous Media

Fattah, Qais Nuri; Hoopes, John A.

doi:10.1061/(asce)0733-9429(1985)111:5(810)

Cited by 56 publications

(26 citation statements)

References 17 publications

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“…The partial differential advection-diffusion equation (ADE) describes water transfer in soils (Parlange, 1980), dispersion of tracers in porous media (Fattah and Hoopes, 1985), the spread of pollutants in rivers and streams (Chatwin and Allen, 1985), the dispersion of dissolved material in estuaries and coastal seas (Holly and Usseglio-Polatera, 1984), contaminant dispersion in shallow lakes (Salmon et al, 1980), the absorption of chemicals into beds (Lapidus and Amundston, 1952), long-range transport of pollutants in the atmosphere (Zlatev et al, 1984), forced cooling by fluids of solid material such as windings in turbo generators (Gane and Stephenson, 1979), thermal pollution in river systems (Chaudhry et al, 1983), flow in porous media (Kumar, 1988) and dispersion of dissolved salts in groundwater (Guvanasen and Volker, 1983). Logan and Zlotnik (1995) proposed analytical solutions with a decay term for periodic input conditions through a semiinfinite domain to address fluctuations of the groundwater table and flow patterns caused by the periodicity of the sea level.…”

Section: Introductionmentioning

confidence: 99%

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

Djordjevich

Savović

Janićijević

2017

Journal of Hydrology and Hydromechanics

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Abstract:The two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finitedifference method for the transport of solutes through a homogenous two-dimensional domain that is finite and porous. Retardation by adsorption, periodic seepage velocity, and a dispersion coefficient proportional to this velocity are permitted. The transport is from a pulse-type point source (that ceases after a period of activity). Included are the firstorder decay and zero-order production parameters proportional to the seepage velocity, and periodic boundary conditions at the origin and at the end of the domain. Results agree well with analytical solutions that were reported in the literature for special cases. It is shown that the solute concentration profile is influenced strongly by periodic velocity fluctuations. Solutions for a variety of combinations of unsteadiness of the coefficients in the advection-diffusion equation are obtainable as particular cases of the one demonstrated here. This further attests to the effectiveness of the explicit finite difference method for solving two-dimensional advection-diffusion equation with variable coefficients in finite media, which is especially important when arbitrary initial and boundary conditions are required.

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Section: Introductionmentioning

confidence: 99%

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

Djordjevich

Savović

Janićijević

2017

Journal of Hydrology and Hydromechanics

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“…It has been used to decsribe heat transfer in a draining film [2], water transfer in soil [3], dispersion of tracers in porous media [4], contaminant dispersion in shallow lakes [5], the spread of solute in a liquid flowing through a tube, longrange transport of pollutants in the atmosphere [6] and dispersion of dissolved salts in groundwater [7]. In the initial works while obtaining the analytical solutions of dispersion problems in the ideal conditions, the basic approach was to reduce the advection-diffusion equation into a diffusion equation by eliminating the advection term(s).…”

Section: Introductionmentioning

confidence: 99%

A Numerical Algorithm for Solving Advection-Diffusion Equation with Constant and Variable Coefficients

Ahmed¹

2012

TONUMJ

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Abstarct: Advection-diffusion equation with constant and variable coefficients has a wide range of practical and industrial applications. Due to the importance of advection-diffusion equation the present paper, solves and analyzes these problems using a new finite difference equation as well as a numerical scheme. The developed scheme is based on a mathematical combination between Siemieniuch and Gradwell approximation for time and Dehghan's approximation for spatial variable. In the proposed scheme a special discretization for the spatial variable is made in such away that when applying the finite difference equation at any time level (j + 1) two nodes from both ends of the domain are left. After that the unknowns at the two nodes adjacent to the boundaries are obtained from the interpolation technique. The results are compared with some available analytical solutions and show a good agreement.

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“…[2,1]. For example, (1.1) has been used to describe heat transfer in a draining film [3], water transfer in soils [4], dispersion of tracers in porous media [5], the intrusion of salt water into fresh water aquifers, the spread of pollutants in rivers and streams [6], the dispersion of dissolved materials in estuaries and coastal seas [7], contaminant dispersion in shallow lakes [8], the absorption of chemicals into beds [9], the spread of solute in a liquid flowing through a tube, long-range transport of pollutants in the atmosphere [10], forced cooling by fluids of solid materials such as windings in turbo generators [11], thermal pollution in river systems [12], flow in porous media [13] and dispersion of dissolved salts in groundwater [14].…”

Section: Introductionmentioning

confidence: 99%

High-order compact solution of the one-dimensional heat and advection–diffusion equations

Mohebbi

Dehghan

2010

Applied Mathematical Modelling

142

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Compact finite difference scheme Parabolic partial differential equations Stability and high accuracy a b s t r a c tIn this work, we propose a high-order accurate method for solving the one-dimensional heat and advection-diffusion equations. We apply a compact finite difference approximation of fourth-order for discretizing spatial derivatives of these equations and the cubic C 1 -spline collocation method for the resulting linear system of ordinary differential equations. The cubic C 1 -spline collocation method is an A-stable method for time integration of parabolic equations. The proposed method has fourth-order accuracy in both space and time variables, i.e. this method is of order Oðh 4 ; k 4 Þ. Additional to high-order of accuracy, the proposed method is unconditionally stable which will be proved in this paper. Numerical results show that the compact finite difference approximation of fourth-order and the cubic C 1 -spline collocation method give an efficient method for solving the one-dimensional heat and advection-diffusion equations.

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Dispersion in Anisotropic, Homogeneous, Porous Media

Cited by 56 publications

References 17 publications

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

A Numerical Algorithm for Solving Advection-Diffusion Equation with Constant and Variable Coefficients

High-order compact solution of the one-dimensional heat and advection–diffusion equations

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