Analytic modeling of two-dimensional transient atmospheric pollutant dispersion by double GITT and Laplace Transform techniques

Cassol, Mariana; Wortmann, Sérgio; Rizza, Umberto

doi:10.1016/j.envsoft.2008.06.001

Cited by 30 publications

(19 citation statements)

References 17 publications

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“…Seven different classes of linear boundary value problems of heat and mass diffusion were studied (Mikhailov and Ozisik 1984), and resulted in the development of three-dimensional general solutions for each of the seven classes of problems by using the generalized integral transform technique (GITT) in the context of separation-of-variable or eigen function expansions. This technique is much used in recent works (Cotta and Mikhailov 1997;Wortmann et al 2005;Cassol et al 2009;Moreira et al 2009). Advectiondiffusion multilayer method (Costa et al 2006) is another method for use in this context.…”

Section: Introductionmentioning

confidence: 96%

One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

et al. 2011

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The one-dimensional linear advection-diffusion equation is solved analytically by using the Laplace integral transform. The solute transport as well as the flow field is considered to be unsteady, both of independent patterns. The solute dispersion occurs through an inhomogeneous semi-infinite medium. Hence, velocity is considered to be an increasing function of the space variable, linearly interpolated in a finite domain in which solute dispersion behaviour is studied. Dispersion is considered to be proportional to the square of the spatial linear function. Thus, the coefficients of the advection-diffusion equation are functions of both the independent variables, but the expression for each coefficient is considered in degenerate form. These coefficients are reduced into constant coefficients with the help of a new space variable, introduced in our earlier works, and new time variables. The source of the solute is considered to be a stationary uniform point source of pulse type.

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Section: Introductionmentioning

confidence: 96%

One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

et al. 2011

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“…They solved the decay chain problem using a semi-analytic approach known as Generalized Integral Transform Technique (GITT), which is a generalization of the Classic Integral Transform Technique, or CITT (Cotta 1993). Very recently, Cassol et al (2009) combined GITT and CITT techniques with Laplace transforms and matrix diagonalization methods to develop an analytical solution for transient two-dimensional atmospheric pollutant dispersion on a semi-infinite spatial domain.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for Multi-Species Contaminant Transport Subject to Sequential First-Order Decay Reactions in Finite Media

Guerrero¹,

Skaggs

Genuchten

2009

Transp Porous Med

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Transport equations governing the movement of multiple solutes undergoing sequential first-order decay reactions have relevance in analyzing a variety of subsurface contaminant transport problems. In this study, a one-dimensional analytical solution for multi-species transport is obtained for finite porous media and constant boundary conditions. The solution permits different retardation factors for the various species. The solution procedure involves a classic algebraic substitution that transforms the advection-dispersion partial differential equation for each species into an equation that is purely diffusive. The new system of partial differential equations is solved analytically using the Classic Integral Transform Technique (CITT). Results for a classic test case involving a three-species nitrification chain are shown to agree with previously reported literature values. Because the new solution was obtained for a finite domain, it should be especially useful for testing numerical solution procedures.

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“…From the methodological point of view, the boundary/initial-value problems for advectiondiffusion equations with variable coefficients that model pollutant dispersion in the atmosphere are usually solved via integral transform-based methods [5,6,19,20,21,34]. Among those methods, the advection-diffusion multilayer method (ADMM) [19,20] provides accurate analytical solutions.…”

Section: Advection-diffusion Equation With Non-local Closurementioning

confidence: 99%

Different Numerical Inversion Algorithms of the Laplace Transform for the Solution of the Advection-Diffusion Equation with Non-local Closure in Air Pollution Modeling

Costa

Rui

Pérez-Fernández

2018

Tend. Mat. Apl. Comput.

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Analytic modeling of two-dimensional transient atmospheric pollutant dispersion by double GITT and Laplace Transform techniques

Cited by 30 publications

References 17 publications

One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

Analytical Solution for Multi-Species Contaminant Transport Subject to Sequential First-Order Decay Reactions in Finite Media

Different Numerical Inversion Algorithms of the Laplace Transform for the Solution of the Advection-Diffusion Equation with Non-local Closure in Air Pollution Modeling

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