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Numerical comparisons of traffic flow models

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Technische Universiteit Eindhoven
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Abstract

Numerical Comparisons of Traffic Flow Models Colette Niyitegeka Supervised by Prof. Dr. Axel Klar (TU Kaiserslautern, Germany) and Dr. J.H.M. ten Thije Boonkkamp (TU Eindhoven, Netherlands) Thesis submitted to the Departments of Mathematics, TU Kaiserslautern and TU Eindhoven in partial fulfillment of the requirements for the award of Master of Science degree in Mathematics Abstract In the past several years, the fast growing number of vehicles on long crowded roads mo- tivated an intense scientific research activity in the field of traffic flow modeling. In this thesis we present and discuss some of the macroscopic models of vehicular traffic flow; the first order LWR model and second order Aw-Rascle model are both solved analytically and numerically. We study the Riemann problems of these models and present some numerical similarities as well as differences between the two models. We perform several numerical experiments in order to verify some qualitative traffic flow behaviour for various traffic pa- rameters in our models. All numerical simulations presented in this thesis are obtained by implementing the first order Godunov-type approximation together with the CFL condition for the stability test of the solutions. In our numerical tests we will show that the Aw-Rascle model predicts instabilities for very light traffic, even with few slow drivers that could not be predicted by the LWR model. Contents 1 Introduction 2 1.1 Motivation and Definition of the Problem . . . . . . . . . . . . . . . . . . . . 2 1.2 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Hyperbolic Systems of Conservation Laws 6 2.0.1 Godunov Scheme for Nonlinear Conservation laws . . . . . . . . . . . 6 2.0.2 The CFL Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.0.3 Consistency of the Godunov Method . . . . . . . . . . . . . . . . . . 9 3 The LWR Model and Its Numerical Solutions 11 3.1 Description of the Mathematical

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