Numerical simulation of two-dimensional pollutant distribution using the Crank-Nicolson method in waste equalization ponds

Abstract

Domestic wastewater flowing from residential areas to wastewater stabilization ponds generally contains various pollutants. In this study, research was conducted to investigate the distribution of pollutants in wastewater ponds by observing changes in biochemical oxygen demand (BOD) parameters. The concentration of pollutant tested was same as the concentration of BOD. The phenomenon of waste particle distribution in domestic wastewater stabilization ponds is viewed as an advection-diffusion scheme. The advection-diffusion scheme can be developed into a mathematical model, specifically a two-dimensional partial differential equation. In this study, numerical methods were used to solve these equations. The Crank-Nicolson method was used to discretize partial differential equations in time and space. The purpose of this study was to determine the points of pollutant dispersion in liquid wastewater stabilization ponds. The dispersion of wastewater pollutants is displayed in simulations performed using Python 3.14.0. The stability analysis of the Crank-Nicolson method is investigated using the Von Neumann method. The results of the analysis show that the Crank-Nicolson method is convergent and unconditionally stable.