Solution to Advection–Dispersion Equation for the Heterogeneous Medium Using Duhamel’s Principle

Pandey, Amit Kumar; Kumar, Rohit; Singh, Mritunjay Kumar

doi:10.1007/978-981-10-5329-0_42

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…Thakur et al [19] obtained exact solutions for two-dimensional solute transport with unsteady dispersion and groundwater velocity in homogeneous and heterogeneous porous media and compared the concentration distribution patterns in the considered media. Pandey et al [20] explored solute transport phenomena in a heterogeneous porous media with Dirichlet type boundary condition by obtaining the solution using Duhamel's Principle.…”

Section: Introductionmentioning

confidence: 99%

“…(7) into one-dimensional or single space variable, we introduce a new transformation as Singh and Chatterjee[21]:We further use following transformation to eliminate convective part of Eq. (12)Applying Laplace Transform Technique to Eqns (17)(18)(19)(20),. one can get the solution of the present problem.…”

mentioning

confidence: 99%

“…one can get the solution of the present problem. For this purpose, we take Laplace Transform of Eqns (17)(18)(19)(20)…”

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confidence: 99%

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Solute Transport Phenomena with Input Through a Plane Surface in Porous Media

Yadav¹,

Roy²

2019

MMEP

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In the present study, analytical solutions for conservative solute transport, originating from a plane input source, along and against the flow is studied in form of two cases through a threedimensional semi-infinite porous media which is bounded between two infinitely spread planes. Also, flow is considered from one plane to another. In first case, concentration gradient perpendicular to the plane which is free from input is considered zero i.e. (ℎ .) • ∧ = 0 while in second case concentration gradient perpendicular to the plane which is free from input is assumed to be proportional to concentration at that plane i.e. (ℎ .) • ∧ ∝. Here ℎ is second order tensor represents dispersion coefficient and ∧ is unit normal vector to the corresponding plane. In both cases, initially the aquifer is supposed to be uniformly polluted. The temporarily dependent dispersion is assumed proportional to the groundwater velocity. The analytical solution of the advection-dispersion equation is obtained using Laplace Transformation Technique. A transformation is used to change the time-dependent advection-dispersion equation into constant coefficients. Such results may be very useful in predicting the concentration pattern in real scenario where the solute material is injected through a plane in a medium. The prosed model may be used to predict concentration profiles of solute in the laboratory as well as in the field.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Solute Transport Phenomena with Input Through a Plane Surface in Porous Media

Yadav¹,

Roy²

2019

MMEP

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A comprehensive review of groundwater vulnerability assessment using index-based, modelling, and coupling methods

Goyal

Haritash

Singh

2021

Journal of Environmental Management

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Reducing the near boundary errors of nonhomogeneous heat equations by boundary consistent methods

Liu

Chang

2020

IMA Journal of Applied Mathematics

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In the paper, we point out a drawback of the Fourier sine series method to represent a given odd function, where the boundary Gibbs phenomena would occur when the boundary values of the function are non-zero. We modify the Fourier sine series method by considering the consistent conditions on the boundaries, which can improve the accuracy near the boundaries. The modifications are extended to the Fourier cosine series and the Fourier series. Then, novel boundary consistent methods are developed to solve the 1D and 2D heat equations. Numerical examples confirm the accuracy of the boundary consistent methods, accounting for the non-zeros of the source terms and considering the consistency of heat equations on the boundaries, which can not only overcome the near boundary errors but also improve the accuracy of solution about four orders in the entire domain, upon comparing to the conventional Fourier sine series method and Duhamel’s principle.

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Solution to Advection–Dispersion Equation for the Heterogeneous Medium Using Duhamel’s Principle

Cited by 3 publications

References 19 publications

Solute Transport Phenomena with Input Through a Plane Surface in Porous Media

Solute Transport Phenomena with Input Through a Plane Surface in Porous Media

A comprehensive review of groundwater vulnerability assessment using index-based, modelling, and coupling methods

Reducing the near boundary errors of nonhomogeneous heat equations by boundary consistent methods

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