The Mathematical Treatment for Air Pollutant Diffusion Using Laplace Adomain Decomposition Method with Ground Surface

Abstract

The method of Laplace Adomain Decomposition has been used to obtain a semi-analytical solution of the threedimensional steady state advection diffusion equation for dispersion of air pollutant from a point source. The present treatment takes into account a realistic boundary condition which considers the ground surface as an absorberreflector surface for the pollutant, simultaneously. This physical consideration is achieved by assuming that the vertical eddy diffusivity coefficient should be non-zero at the ground surface for vertical diffusion to be possible. The wind prevailing speed is parameterized in terms of vertical height using the power law profile. An upper boundary condition assuming capping inversion is considered which means that pollutant is subjected to a boundary Condition of zero flux. The present model calculations are compared with the available data of the atmospheric dispersion experiments that were carried out in the Copenhagen area (Denmark) and the semi-empirical model for Gaussian plume model with the same input data. In both comparison tasks, the results are reasonably good which indicates that the present treatment performs well as a simple analytical dispersion model.