Numerical Solutions To Nonlinear Hyperbolic Systems Of Conservation Laws Applied To Traffic Flow Theory Research Report in Mathematics, Number 29, 2020

Abstract

In the recent past, the rapid growing number of vehicles on long crowded roads elicited rigorous scienti c research activities in the eld of tra c ow modeling. In this thesis we present and discuss some of the macroscopic models of vehicular tra c ow; here we discuss Payne-Whitham(P-W) and the Aw-Rascle models of tra c ow both of which are second order. We study the Riemann problems of these models. The numerical method developed here is the nite volume method (FVM), more speci cally the Godunov-type approximation together with the CFL condition for stability test of solutions.