Riemann Problem Resolution and Godunov Scheme for the Aw-Rascle-Zhang Model

Recently, Aw and Rascle and Zhang introduced a new second-order macroscopic model, following the theoretical investigations on the Payne-Whitham second-order modelling by Daganzo. The conserved variables in this model are the density and the relative flow. The aim of this paper is to solve the Riema...

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Bibliographic Details
Published in:Transportation science 2009-11, Vol.43 (4), p.531-545
Main Authors: Mammar, Salim, Lebacque, Jean-Patrick, Salem, Habib Haj
Format: Article
Language:English
Subjects:
analytical solutions
Applied sciences
Cauchy problem
Computational methods
Conservation laws
Construction
contact discontinuities
Density
discretisation
Elastic waves
Exact sciences and technology
Ground, air and sea transportation, marine construction
Initial conditions
Logistics
Macroscopic models
Mathematical analysis
Mathematical economics
Mathematical models
Modeling
Numerical analysis
numerical solutions
Operations research
Problem solving
rarefaction waves
Riemann problem
Road transport
Road transportation and traffic
shock waves
Studies
Traffic
Traffic estimation
Traffic flow
Traffic models
Traffic speed
Transport economics
Transportation
Transportation planning, management and economics
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Summary:Recently, Aw and Rascle and Zhang introduced a new second-order macroscopic model, following the theoretical investigations on the Payne-Whitham second-order modelling by Daganzo. The conserved variables in this model are the density and the relative flow. The aim of this paper is to solve the Riemann problem for the Aw-Rascle-Zhang (ARZ) model for all possible initial conditions, using an extended fundamental diagram. The resolution of the Riemann problem provides the user of the model with a set of nontrivial analytical solutions; it is also a prerequisite for the construction of numerical solution schemes. Some examples are given in which analytical solutions of the Riemann problem are discussed and compared to numerical solutions. The ARZ model shows better fit to real data than the embedded Lighthill-Whitham-Richards (LWR) model for the same set of physical parameters.
ISSN:0041-1655
1526-5447
DOI:10.1287/trsc.1090.0283