Air Pollution Steady-State Advection-Diffusion Equation: The General Three-Dimensional Solution

Daniela Buske, Marco Túllio Vilhena, Tiziano Tirabassi, Bardo Bodmann

Department of Mathematics and Statistics (IFM/DME), Federal University of Pelotas (UFPel), Pelotas, Brazil.
Graduate Program in Mechanical Engineering, Federal University of Rio Grande do Sul (UFRGS), Porto Alegre, Brazil.
Institute of Atmospheric Sciences and Climate (ISAC), National Research Council (CNR), Bologna, Italy.

DOI: 10.4236/jep.2012.329131                

Abstract

Atmospheric air pollution turbulent fluxes can be assumed to be proportional to the mean concentration gradient. This assumption, along with the equation of continuity, leads to the advection-diffusion equation. Many models simulating air pollution dispersion are based upon the solution (numerical or analytical) of the advection-diffusion equation as- suming turbulence parameterization for realistic physical scenarios. We present the general steady three-dimensional solution of the advection-diffusion equation considering a vertically inhomogeneous atmospheric boundary layer for arbitrary vertical profiles of wind and eddy-diffusion coefficients. Numerical results and comparison with experimental data are shown.

Keywords

Advection-Diffusion Equation; Analytical Solution; Laplace Transform; Air Pollution Modeling; Atmospheric Boundary Layer; Eulerian Models

Conflicts of Interest

The authors declare no conflicts of interest.

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