Title: A solution of the time-dependent advection-diffusion equation

Authors: Tiziano Tirabassi; Everson J.G. Silva; Daniela Buske; Marco T. Vilhena

Addresses: Institute ISAC of CNR, Via Gobetti 101, Bologna, Italy; Federal University of Santa Maria (UFSM), Av. Roraima 1000, Santa Maria (RS), CEP:97105-900, Brazil ' Federal University of Pampa (UNIPAMPA), Av. Maria Anunciação Gomes de Godoy, 1650, Bagé (RS),CEP: 96413-172, Brazil ' Federal University of Pelotas (UFPel), Campus Universitário, s/nº, Pelotas (RS), CEP: 96010-900, Brazil ' Federal University of Rio Grande do Sul (UFRGS), Osvado Aranha, 99, Porto Alegre (RS), CEP: 90046-900, Brazil

Abstract: We present an analytical solution that considers time dependence in the wind profile and the eddy diffusivity. The solution accepts any profiles of wind and eddy coefficient diffusions in a limited planetary boundary layer. The solution is based on the idea of a decomposition method upon expanding the pollutant concentration in a truncated series. This produces a set of recursive equations whose solutions are known. Each equation of this set is solved by the generalised integral Laplace transform technique (GILTT) method. The solution's ability to represent real situations was checked, comparing model predictions with the over-land along-wind dispersion (OLAD) experimental dataset.

Keywords: air pollution modelling; advection-diffusion equation; analytical solution; environment management; air pollution; decomposition.

DOI: 10.1504/IJEP.2019.101842

International Journal of Environment and Pollution, 2019 Vol.65 No.1/2/3, pp.211 - 228

Received: 22 Dec 2017
Accepted: 07 Jan 2019

Published online: 22 Aug 2019 *

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