Analytical solutions of nonlinear and variable-parameter transport equations for verification of numerical solvers

Zamani, Kaveh; Bombardelli, Fabián A.

doi:10.1007/s10652-013-9325-0

Cited by 35 publications

(21 citation statements)

References 74 publications

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“…(33) and then using Eq. (16), the desired solution may be written as Jaiswal et al [26], Yadav et al [27], Yadav et al [28]: Concentration pattern is evaluated along these mentioned directions PQ, PR and PS at times ( ) 0.08 t year = and 0.5 .…”

Section: Case 1 Input In Direction the Flowmentioning

confidence: 99%

“…Park and Zhan [15] derived general form of analytical solutions of solute transport from threedimensional sources in a finite thickness aquifer using Green Function Method. Zamani and Bombardelli [16] proposed analytical solutions of nonlinear advection-dispersion equation with spatially and temporally dependent dispersion coefficient and velocity. Kumar et al [17] obtained solution for a two-dimensional solute transport problem with spatially varying dispersion and groundwater velocity.…”

Section: Introductionmentioning

confidence: 99%

“…i.ein Eq. (27b) it reduces to condition of boundary condition against the flow Jaiswal et al[26], Yadav et al[27], Yadav et al[28].Applying transformations in Eqns (6,11,16),. Eqns.…”

mentioning

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: Case 1 Input In Direction the Flowmentioning

confidence: 99%

Section: Introductionmentioning

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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“…This model is more advanced than any of the other models developed before. Zamani and Bombardelli (2014) presented analytical solutions for transport of non-reactive species in unsaturated soil. Zamani and Ginn (2017) reviewed the state of art of pollutant transport in vadose zone as well as numerical models, including SUTRA (Voss and Provost 2002), VS2DT (Healy 1990), HYDRUS (Radcliffe and Simunek 2010), among others.…”

Section: Pollutant Transportmentioning

confidence: 99%

Hydrologic modeling: progress and future directions

Singh

2018

Geosci. Lett.

123

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Briefly tracing the history of hydrologic modeling, this paper discusses the progress that has been achieved in hydrologic modeling since the advent of computer and what the future may have in store for hydrologic modeling. Hydrologic progress can be described through the developments in data collection and processing, concepts and theories, integration with allied sciences, computational and analysis tools, and models and model results. It is argued that with the aid of new information gathering and computational tools, hydrology will witness greater integration with both technical and non-technical areas and increasing applications of information technology tools. Furthermore, hydrology will play an increasingly important role in meeting grand challenges of the twenty-first century, such as food security, water security, energy security, health security, ecosystem security, and sustainable development.

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“…You and Zhan (2013) studied the semi-analytical solution for solute transport in a finite column with linear asymptotic or exponen-tial distance-dependent dispersivities and time-dependent sources. Zamani and Bombardelli (2014) explored analytical solutions to the ADR (advection-dispersion-reaction) equation from which one can know the spatio-temporal changes in flow field and dispersivity. Van Genuchten et al (2013) presented a series of one-and multi-dimensional solutions of the standard equilibrium advection-dispersion equation with and without terms accounting for zero-order production and first-order decay, which proved useful for simplified analyses of contaminant transport in surface water, and for mathematical verification of more comprehensive numerical transport models where the isotherm concept was not used.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of groundwater contamination with varying velocity field

Das

Begam

Singh

2017

Journal of Hydrology and Hydromechanics

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Abstract:In this study, analytical models for predicting groundwater contamination in isotropic and homogeneous porous formations are derived. The impact of dispersion and diffusion coefficients is included in the solution of the advection-dispersion equation (ADE), subjected to transient (time-dependent) boundary conditions at the origin. A retardation factor and zero-order production terms are included in the ADE. Analytical solutions are obtained using the Laplace Integral Transform Technique (LITT) and the concept of linear isotherm. For illustration, analytical solutions for linearly space-and time-dependent hydrodynamic dispersion coefficients along with molecular diffusion coefficients are presented. Analytical solutions are explored for the Peclet number. Numerical solutions are obtained by explicit finite difference methods and are compared with analytical solutions. Numerical results are analysed for different types of geological porous formations i.e., aquifer and aquitard. The accuracy of results is evaluated by the root mean square error (RMSE).

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Analytical solutions of nonlinear and variable-parameter transport equations for verification of numerical solvers

Cited by 35 publications

References 74 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

Hydrologic modeling: progress and future directions

Mathematical modeling of groundwater contamination with varying velocity field

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