Dispersion of pollutants based on a reaction-diffusion model

Dispersion of pollutants is a central topic in atmospheric modeling as well as in environmental weather hazards management. A considerable body of evidences exists in the scientific literature regarding the impact of different chemical species and particulate matter on human health (cardio-respiratory diseases). Approaches based on meso-scale models as WRF-Chem and CMAQ have provided very good insights about the spreading and the reactivity of different chemical species within the atmosphere. However, the downscaling of these calculations to urban environments is still pending to be solved. Computational Fluid Dynamics (CFD) calculations are very good at these scales, and some hybrid approaches overlapping these two limits are in use. On the other end, the solution of the linear equation of diffusion has permitted to track the concentration of pollutants in the form of a Gaussian function and understand the overall spatial distribution of them. Motivated by these facts, in this communication, a reaction – diffusion model consisting of three interacting species is discussed. Reaction-diffusion mathematical models combine in a single framework the local chemical reactions between species in which substances are transformed into each other and diffusion, which cause them to spread out over a surface in space. In urban biometeorology reaction-diffusion models in bounded regions are very important in order to analyze the impact of urban canyons on the spatial distribution of chemical species. In this communication CO, NOx, and O3 were selected as model species. Even though, it is a very simplified model for the chemistry of the atmosphere, as well as for the entire dynamics of the atmosphere it focuses on the different diffusivity of species, their reactivity, and the non – linear character of the processes. Three models are explored: Fisher's equation, Newell-Whitehead-Segel equation, and Zeldovich equation. The current state of the atmosphere is introduced via external forcing to the equation with different amplitudes and frequencies.