Integral transform solutions for atmospheric pollutant dispersion

A transient two-dimensional advection–diffusion model describing the turbulent dispersion of pollutants in the atmosphere has been solved via the Generalized Integral Transform Technique (GITT), by two different schemes. The first approach performs numerical integration of the transformed system using available routines for initial value problems with automatic error control. In spite of the time-consuming character of such a scheme, its flexibility allows the handling of problems involving time-dependent meteorological parameters such as wind speed and eddy diffusivities. The second approach works fully analytically being thus intrinsically more robust and economic, although not directly applicable in dealing with time-dependent parameters. For the test problem used in this work, both methods agree very well with each other, as well as with a known analytical solution for a simpler formulation used as benchmark. The impact of the longitudinal diffusivity on the stiffness of the ordinary differential equation (ODE) system arising from the integral transformation has been assessed through the processing time demanded to solve it when the numerical approach is used. The observed CPU times show that the analytical approach is clearly preferable unless the problem involves time-dependent parameters.