Modelagem da qualidade do ar: revisão de modelos e proposta para a consideração do efeito da movimentação de fontes móveis

Abstract

The main purpose of this research was to achieve an analytical mathematical model to simulate the atmospheric pollution caused by a non-stationary pollution point source moving at constant speed. The pollutant considered is passive and conservative. The effort to find such a solution was partly due to the fact that a literature review was not able to find a mathematical model presenting this capability. The derivation of this model is presented step by step, beginning with the derivation of the advective-diffusion equation, or the mass transport equation, for the particular case of constant velocity and homogeneous and anisotropic turbulent diffusion. Then, a general solution for this equation was achieved, considering a generic source/sink term. This was obtained with the use of the Complex Fourier Transform, as presented in detail here. This general solution was then compared by applying it to cases found in the literature, as the emission from stationary point sources in steady and unsteady flow and the so called gaussian plume model. Those solutions were recovered from the general solution obtained here. By considering the appropriate source sink/term for the situation of a point source moving at constant speed, the corresponding solution was finally obtained. Then, some properties of this solution were presented.