One-dimensional uniform and time varying solute dispersion along transient groundwater flow in a semi-infinite aquifer

Singh, Mritunjay Kumar; Ahamad, Shafique; Singh, Vijay P.

doi:10.2478/s11600-014-0208-7

Cited by 7 publications

(2 citation statements)

References 17 publications

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“…The values of common input parameters such as ground water velocity, dispersion coefficient, first order decay etc. are taken from published literature [26][27][28][29]. The concentration values are evaluated assuming reference concentration as 𝐶 0 = 1.0, 𝐶 𝑖 = 0.01 in a finite domain along longitudinal direction.…”

Section: Resultsmentioning

confidence: 99%

Numerical Solution for Advection-Dispersion Equation with Uniform and Varying Boundary Conditions

Kumar¹,

Yadav²,

Roy³

et al. 2022

EESRJ

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In the present study, one-dimensional advection-dispersion equation with variable coefficients is solved numerically with help of PDEPE in a finite porous domain. The pollutant is entering from the left end of the domain along the direction of the flow. Two different types of groundwater velocities have been considered, one rapidly decreasing with position and time and the other one being of sinusoidal nature over position and time. The dispersion coefficient is taken proportional to the groundwater velocity. Transport is included the first order decay and zero-order production parameters being proportional to the exponentially decreasing function with position and time and also being of sinusoidal nature over position and time. The nature of pollutant and porous medium are considered chemically non-reactive. Initially, porous domain is considered not to be solute free. Numerical solutions are obtained for uniform and varying type point sources. In heterogeneous porous media, variations in the parameters of solute transport such as: seepage velocities, dispersion coefficients etc. can be easily deal through numerical models. The effects of various physical parameters on solute concentration profiles are illustrated graphically.

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Section: Resultsmentioning

confidence: 99%

Numerical Solution for Advection-Dispersion Equation with Uniform and Varying Boundary Conditions

Kumar¹,

Yadav²,

Roy³

et al. 2022

EESRJ

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“…Singh et al [10] obtained analytical solutions for onedimensional solute dispersion with uniform and time varying dispersion in a semi-infinite aquifer using the Laplace transform technique. Falta and Wang [11] presented a semianalytical solution of one-dimensional advection-dispersion equation with matrix diffusion process by assuming the low permeability in semi-infinite domain.…”

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Solute Transport with Multiple Point Sources in Semi-infinite Porous Media

Yadav¹,

Kumar²

2020

IJES

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In the present study, analytical solutions have been developed for two-dimensional solute transport in steady field of groundwater flow with different longitudinal and lateral dispersion coefficients in semi-infinite heterogeneous porous medium for a varying type input point source. Dispersion coefficient is considered squarely proportional to the groundwater velocity along both longitudinal and lateral directions while groundwater velocity is considered linear spatially dependent function in both directions. The flow is assumed to be two-dimensional in a horizontal plane and the nature of pollutant and porous medium are considered chemically non-reactive. The geological formation is initially not solute free. Varying type input condition for multiple point sources through arbitrary time-dependent function is considered at origin. Concentration gradient is considered zero at infinity. New space variables are introduced by certain transformations to get the analytical solutions. The solutions in the real time domain are obtained by using Laplace Integral Transform Technique. The obtained analytical solutions are illustrated graphically to study the effect of various parameters on the solute transport in various time domains for spatially dependent velocity.

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Mathematical Modeling of One-Dimensional Advection Dispersion Equation in Groundwater Contamination Using Different Velocity and Dispersion for Different Zones

Singh

Chatterjee

Kumari³

2017

Lecture Notes in Mechanical Engineering

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One-dimensional uniform and time varying solute dispersion along transient groundwater flow in a semi-infinite aquifer

Cited by 7 publications

References 17 publications

Numerical Solution for Advection-Dispersion Equation with Uniform and Varying Boundary Conditions

Numerical Solution for Advection-Dispersion Equation with Uniform and Varying Boundary Conditions

Two-Dimensional Solute Transport with Multiple Point Sources in Semi-infinite Porous Media

Mathematical Modeling of One-Dimensional Advection Dispersion Equation in Groundwater Contamination Using Different Velocity and Dispersion for Different Zones

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