MODELLING TRAFFIC FLOW BEFORE AND AFTER ROUNDABOUT USING NAVIER-STOKES AND ADVECTION-DIFFUSION EQUATIONS

Abstract

Traffic congestion remains a persistent challenge in urban areas, with roundabouts playing a pivotal role in enhancing road safety, improving traffic flow, and minimizing congestion. Understanding traffic dynamics before and after roundabout implementation is critical for optimizing urban infrastructure. Traditional traffic models lack the precision to account for the complex interactions and flow disruptions associated with roundabouts. These limitations hinder accurate predictions of traffic patterns, requiring more advanced mathematical approaches to model flow dynamics effectively. This study aims to model traffic flow around roundabouts using Navier-Stokes and advection-diffusion equations. Specific objectives include formulating mathematical models, analyzing the influence of roundabout geometry on traffic flow, evaluating disruption and diffusion effects, and identifying critical factors impacting flow stability. The study employed fluid mechanics principles, utilizing the Navier-Stokes and advection-diffusion equations to model traffic as a fluid-like system. Numerical simulations were conducted using the Finite Volume Method and Crank-Nicolson scheme, with Matlab R2023b facilitating sensitivity analyses to evaluate various scenarios. Findings indicate that roundabouts significantly improve traffic flow efficiency by reducing congestion and enhancing speed regulation. The geometric design of roundabouts and their capacity to handle disruptions were identified as key factors influencing performance. Sensitivity analysis revealed optimal configurations for minimizing delays and maximizing output. The integration of roundabouts enhances urban traffic dynamics by mitigating congestion and optimizing vehicle movement. Mathematical models provide a robust framework for analyzing these effects, ensuring informed urban planning. Policymakers should incorporate advanced mathematical modeling in roundabout designs, emphasizing scenario-specific analyses to address diverse traffic conditions. Future research should integrate behavioral and environmental factors to refine predictive capabilities and practical applications