THREE – DIMENSIONAL POLLUTANT TRANSPORT WITH TURBULENCE EFFECT: MODELING AND SOLUTIONS

Abstract

This paper presents a model for estimating pollutant concentrations by incorporating the effects of advection, diffusion, and turbulence along each coordinate axis. While the classical advection-diffusion equation (ADE) accounts for pollutant transport under the combined influence of advection and diffusion, the proposed model extends this by including turbulence effects. Despite the challenges of deriving an analytical solution, we achieve one using the Eigenfunction expansion method under specific initial and boundary conditions assuming idealized situation. To address real-world scenarios with complex boundaries, a numerical solution is computed using the Alternating Direction Implicit (ADI) method, demonstrating its superiority over alternative numerical techniques. Furthermore, we investigate the influence of eddy diffusivity and time on concentration in realistic scenarios, assess numerical accuracy via L₂ norm and Root Mean Square Error (RMSE), and present results through 3D visualizations. This work demonstrates that analytical and numerical methods effectively estimate pollutant concentrations under turbulence and are essential for evaluating impacts and guiding pollution control policies.