Analytical solutions of the one-dimensional advection–dispersion solute transport equation subject to time-dependent boundary conditions

Guerrero, J.S. Pérez; Pontedeiro, Elizabeth M.; Genuchten, Martinus Th. van; Skaggs, Todd H.

doi:10.1016/j.cej.2013.01.095

Cited by 82 publications

(21 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several approaches, in addition to moving coordinate transformation and product rules, have been used in the literature. These include separation of variables and Fourier series (Bruch and Street, 1967), Green's functions Sagar, 1982;Yeh and Tsai, 1976), or integral transforms (Cleary, 1973;Leij and Dane, 1990;Leij et al, 1993, Pérez Guerrero et al, 2013.…”

Section: Problems In Several Dimensionsmentioning

confidence: 99%

Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation

Genuchten¹,

Leij²,

Skaggs³

et al. 2013

Journal of Hydrology and Hydromechanics

View full text Add to dashboard Cite

Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-water hydrology, are scattered across the literature, and not always well known. In this two-part series we provide a discussion of the advection-dispersion equation and related models for predicting concentration distributions as a function of time and distance, and compile in one place a large number of analytical solutions. In the current part 1 we present 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. The solutions may prove useful for simplified analyses of contaminant transport in surface water, and for mathematical verification of more comprehensive numerical transport models. Part 2 provides solutions for advective-dispersive transport with mass exchange into dead zones, diffusion in hyporheic zones, and consecutive decay chain reactions.

show abstract

Section: Problems In Several Dimensionsmentioning

confidence: 99%

Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation

Genuchten¹,

Leij²,

Skaggs³

et al. 2013

Journal of Hydrology and Hydromechanics

View full text Add to dashboard Cite

show abstract

“…This class of problems has motivated studies pursuing analytical solutions of convection-diffusion-reaction equation subjected to time-dependent BCs, like the ones from van Genuchten and Alves (1982), Logan and Zlotnik (1995), Logan (1996), Aral and Liao (1996), Golz and Dorroh (2001), Chen and Liu (2011) and Pérez Guerrero et al (2013). However, these studies either are restricted to 1-D cases, or adopt conditions that may not represent time dependence close to the domain exit.…”

Section: Scopementioning

confidence: 99%

Simulation of species concentration distribution in reactive flows with unsteady boundary conditions

Filho

Mangiavacchi

Pontes

2017

Braz. J. Chem. Eng.

View full text Add to dashboard Cite

-The determination of species concentration profiles in reactive flows with variable inlets is a problem of practical interest to many fields such as in flow reactor transient operation and in cyclic degradable pollutants disposals in watercourses. In these cases, the inflow condition often consists of a time-dependent function, which may imply unsteady outflows, not always well represented by the usual boundary conditions (BC) used so far. A new approach, using an outlet condition in the form of a material derivative, termed Material Derivative Boundary Condition (MDBC), is introduced and a numerical model to solve convection-diffusion-reaction equations in twodimensional (2-D) incompressible flows is developed. Upon reviewing the literature, it is noted that the Finite Element Method (FEM) is rarely used in the simulation of reactive flows, in spite of its ability of consistently coping with variable BCs. The above facts are reasons to explore its use along with a semi-discrete formulation with the Galerkin Method in our simulations. Results are obtained for various conditions, in order to show features of the code, and are compared to existing solutions. Use of the MDBC is shown to provide a better approximation of the exit concentrations and use of FEM in reactive flows is further enhanced.

show abstract

“…For t>t 0 , we have the following boundary conditions: c(0,t)= f (t) and, at the outflow, we assume continuous concentration, forcing an homogeneous Neumann exit, which is also referred to as Danckwerts condition in finite transport domains [2,5,7]. Assuming that f (t) is time periodic and has a Fourier representation, we may consider that Eq.…”

Section: Analytic Solution For the 1d Transient Problemmentioning

confidence: 99%

“…Among them, it can be found in the works by van Genuchten and Alves [6], Logan and Zlotnik [4], Logan [3], Goltz and Dorroh [2], Ziskind et al [7], Chen and Liu [1] and Pérez Guerrero et al [5], analytical solutions pertaining to time varying boundary conditions, which is of practical interest to many fields as hydrogeology, pollution dispersion and process industry.…”

Section: Introductionmentioning

confidence: 99%

Multidimensional Unsteady Solutions to the Convection-Diffusion-Reaction Equation with a Time Dependent Boundary Condition

Filho¹,

Mangiavacchi²

2017

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

View full text Add to dashboard Cite

Abstract. This paper provides analytical solutions to one, two and three-dimensional convection-diffusion equation with decay term, subjected to a time dependent and periodic boundary condition. These solutions are suitable benchmarks to asses the correctness of computational codes implemented for the problems of multidimensional reactive flows, which are of considerable interest to many fields of science and engineering. Tests are illustrated through computational codes and is remarked the feature of representing periodic oscillations in all dimensions considered.

show abstract

Analytical solutions of the one-dimensional advection–dispersion solute transport equation subject to time-dependent boundary conditions

Cited by 82 publications

References 21 publications

Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation

Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation

Simulation of species concentration distribution in reactive flows with unsteady boundary conditions

Multidimensional Unsteady Solutions to the Convection-Diffusion-Reaction Equation with a Time Dependent Boundary Condition

Contact Info

Product

Resources

About