Daniela Buske

A General Analytical Solution of the Advection–Diffusion Equation for Fickian Closure

In the last few years there has been increased research interest in searching for analytical solutions for the advection–diffusion equation (ADE). By analytical we mean that no approximation is done along the derivation of the solution. There exists a significant literature regarding this theme. For illustration we mention the works of (Rounds 1955; Smith 1957; Scriven, Fisher 1975; Demuth 1978; van Ulden 1978; Nieuwstadt, de Haan 1981; Tagliazucca et al. 1985; Tirabassi 1989; Tirabassi, Rizza 1994; Sharan et al. 1996; Lin, Hildemann 1997; Tirabassi 2003). We note that in these works all solutions are valid for very specialized problems having specific wind and eddy diffusivities vertical profiles. Further, also in the literature there is the ADMM (Advection Diffusion Multilayer Method) approach which solves the two-dimensional ADE with variable wind profile and eddy diffusivity coefficient (Moreira et al. 2006). The main idea relies on the discretization of the Atmospheric Boundary Layer (ABL) in a multilayer domain, assuming in each layer that the eddy diffusivity and wind profile take averaged values. The resulting advection–diffusion equation in each layer is then solved by the Laplace transformation technique. For more details about this methodology see the review work done by (Moreira et al. 2006). We are also aware of the recent work of (Costa et al. 2006), dubbed as GIADMT method (Generalized Integral Advection Diffusion Multilayer Technique), which presented a general solution for the time-dependent three-dimensional ADE, again assuming the stepwise approximation for the eddy diffusivity coefficient and wind profile and proceeding further in similar way according the previous work. To avoid this approximation, in this work we report an analytical general solution for this problem, assuming that the eddy diffusivity coefficient and wind profile are arbitrary functions having a continuous dependence on the vertical and longitudinal variables. Without losing generality we specialize the application in micrometeorology, specially for the problem of simulation of contaminant releasing in the ABL.

An Analytical Solution for the Transient Two-Dimensional Advection–Diffusion Equation with Non-Fickian Closure in Cartesian Geometry by the Generalized Integral Transform Technique

Analytical solutions of equations are of fundamental importance in understanding and describing physical phenomena, since they are able to take into account all the parameters of a problem and investigate their influence. In a recent work, [Bus07] reported an analytical solution for the stationary two-dimensional advection–diffusion equation with Fickian closure by the Generalized Integral Laplace Transform Technique (GILTT). The main idea of this method consists of: construction of an auxiliary Sturm–Liouville problem, expansion of the contaminant concentration in a series in terms of the obtained eigenfunctions, replacement of the expansion in the original equation, and finally after taking moments, resulting a set of ordinary differential equations which are then solved analytically by the Laplace transform technique.

SIMULATION OF A MODEL OF DISPERSION OF POLLUTION WITH CHEMICAL REACTION IN THE ATMOSPHERIC BOUNDARY LAYER

This work presents an analytical representation for a dispersion model of pollutants that considers the chemical reaction, the model uses the three-dimensional advection-diffusion equation to describe the concentration field in the atmospheric boundary layer and to represent the chemical reaction that the pollutant suffers is included a source term in the equation. To solve the problem we use the modified Adomian Decomposition method associated with the 3D-GILTT method. The model was applied to simulate the dispersion and transportation of the

POLLUTANTS DISPERSION SIMULATION IN AN EULERIAN MODEL CONSIDERING EDDY DIFFUSIVITIES THAT DEPEND OF THE SOURCE DISTANCE AND THE WIND MEANDERING PHENOMENON

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A SIMPLE FORMULA FOR THE EVALUATION OF VALUE AND POSITION OF GROUND LEVEL CONCENTRATION FROM A POINT SOURCE

(sulfur dioxide), a pollutant produced from the burning of mineral coal, emitted by the Presidente Medici thermoelectric plant, located in Candiota / RS. With the analysis of the results it can be observed that the concentrations generated by the model are satisfactory and that the approach used is a new proposal for the description of the concentration field of a substance.

Eddy diffusivities for the convective boundary layer derived from LES spectral data

The aim of this work is to simulate the pollutants dispersion in an Eulerian model considering the wind meandering phenomenonxa0and eddy diffusivities in terms of source distance. The pollutants dispersion model solve analytically the adcevction-diffusionxa0equation by 3D-GILTT technique. To consider the wind meandering in the dispersion model, we decompose the wind in the u and v components and we calculate the autocorrelation functions and wind spectra. The results show a good agreement between thexa0observed and simulated concentrations.

A Closed Form Solution for Pollutant Dispersion Simulation in Atmosphere Under Low Wind Conditions

After setting realistic scenarios of the wind and diffusivity parameterizations the Ground Level Concentration is worked out by an analytical solution of the advection-diffusion equation, then an explicit approximate expression is provided for it allowing a simple expression for the position and value of the maximum.

An Analytical Model for Contaminant Dispersion Release in the Atmospheric Boundary Layer Considering Time Variable Eddy Diffusivity

Large Eddy Simulation (LES) spectral data and Taylor statistical diffusion theory are used to obtain Eddy diffusivities in a convective boundary layer. The derivation employs a fitting expression obtained from LES data for the vertical peak frequency. The vertical Eddy diffusivities are well behaved and show similar patterns and magnitudes as those derived from experimental spectral peak frequency data. In addition, this new vertical Eddy diffusivity was introduced into an advection diffusion equation which was solved by Generalized Integral Laplace Transform Technique (GILLT) method and validated with observed contaminant concentration data of the Copenhagen experiment. The results of this new approach are shown to agree with the measurements of Copenhagen.

Eddy Diffusivity to North Wind Phenomenon in Southern Brazil: Application in an Analytical Dispersion Model

The present study proposes a mathematical model for dispersion of contaminants in low winds that takes into account the along-wind diffusion. The solution of the advection-diffusion equation for these conditions is obtained applying the 3D-GILTT method. Numerical results and comparison with experimental data are presented.

Some characteristics of a plume from a point source based on analytical solution of the two-dimensional advection-diffusion equation

In this work we present a new model and simulations for more realistic scenarios incorporating in the diffusive model the dependence of the eddy diffusivity profile on the temporal variable. Numerical results and comparison with experimental data are presented.