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.
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Donat, R., Mulet, P. Characteristic-Based Schemes for Multi-Class Lighthill-Whitham-Richards Traffic Models. J Sci Comput 37, 233–250 (2008). https://doi.org/10.1007/s10915-008-9209-5
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DOI: https://doi.org/10.1007/s10915-008-9209-5