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.
In this chapter, pursuing the task of searching analytical solutions, we start by presenting an analytical solution for the transient two-dimensional advection–diffusion equation with non-Fickian closure in Cartesian geometry by the GILTT method. We specialize the application of this methodology to the simulation of pollutant dispersion in the planetary boundary layer (PBL) under low wind conditions. We also present numerical results and comparison with experimental data.
KeywordsPlanetary Boundary Layer Convective Boundary Layer Pollutant Dispersion Liouville Problem Lagrangian Time Scale
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