Characteristic-Based Schemes for Multi-Class Lighthill-Whitham-Richards Traffic Models

Authors:
Rosa Donat;Pep Mulet
Affiliations:
Departament de Matemàtica Aplicada, Universitat de València, Burjassot, Spain 46100;Departament de Matemàtica Aplicada, Universitat de València, Burjassot, Spain 46100
Venue:
Journal of Scientific Computing
Year:
2008

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Abstract

In this paper we provide the full spectral decomposition of the Multi-Class Lighthill Whitham Richards (MCLWR) traffic models described in (Wong et al. in Transp. Res. Part A 36:827---841, 2002; Benzoni-Gavage and Colombo in Eur. J. Appl. Math. 14:587---612, 2003). Even though the eigenvalues of these models can only be found numerically, the knowledge of the spectral structure allows the use of characteristic-based High Resolution Shock Capturing (HRSC) schemes. We compare the characteristic-based approach to the component-wise schemes used in (Zhang et al. in J. Comput. Phys. 191:639---659, 2003), and propose two strategies to minimize the oscillatory behavior that can be observed when using the component-wise approach.