Mathematical Modeling of Pollutant Dispersion in Turbulent Airflows of the Atmospheric Boundary Layer
Abstract
The paper presents a mathematical model of pollutant dispersion in turbulent airflows within the atmospheric boundary layer. The model is based on the advection–diffusion equation and the system of Navier–Stokes equations, complemented by the ???? − ???? turbulence model. In this formulation, the model provides an accurate description of the spatiotemporal dynamics of pollutant concentration. A point emission source is introduced through the Dirac delta function, which makes it possible to correctly represent localized pollutant releases. For the numerical solution of the problem, an algorithm based on a finite-difference scheme with directional (upwind) flux approximation and iterative pressure correction using the conjugate gradient method is proposed. Boundary and initial conditions are formulated for the near-surface atmospheric layer, taking into account the spatial inhomogeneity of the wind field and the vertical gradient of turbulent energy. The developed model ensures a stable solution and can be applied to analyze pollutant dispersion dynamics, forecast air quality, and optimize urban ventilation systems under various meteorological conditions.