One Dimensional Contaminant Transport with Turbulence Effect: Modeling and Solutions - Poudel, Eeshwar Prasad; Khadka, Shree Ram; Kafle, Jeevan (Journal of Nepal Mathematical Society, 2025)
This paper presents a one-dimensional model for atmospheric contaminant transport that accounts for advection, diffusion, and turbulence effects. The classical advection-diffusion equation is extended through Reynolds decomposition and hence averaging to incorporate turbulence via eddy diffusivity. While analytical solutions for such models are typically intractable under real-world conditions with complex boundaries, we derive an exact solution for idealized cases with general initial condition and Dirichlet boundary conditions, providing a valuable benchmark for numerical validation. To address more realistic scenarios, numerical solutions are developed using finite difference (FD) and Crank-Nicolson (CN) methods. This study explores the impact of eddy diffusivity and temporal dynamics on pollutant concentrations within idealized scenarios, benchmarking numerical methods against a derived analytical solution. The analysis reveals that the CN method outperforms FD method in accuracy, particularly in diffusion-dominated regimes (Pe