Abstract
In this paper a second order vehicular macroscopic model is derived from a microscopic car–following type model and it is analyzed. The source term includes nonlocal anticipation terms. A Finite Volume Lagrange–remap scheme is proposed.
MSC2010: 65M08, 65M22, 65P40, 65Y20, 65Z05
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Aw and M. Rascle, Resurrection of “second order” models of traffic flow. SIAM J. Appl. Math., Vol. 60 (3),(2000), 916-938.
A. Aw, A. Klar, T. Materne, and M. Rascle. Derivation of continuum traffic flow models from microscopic follow-the-leader models, SIAM J. Applied Math., 63 (1), 259–278 (2002).
M. Bando, K. Hasebe, A. Nakayama, A. Shibata, Y. Sugiyama, Phys. Rev. E 51, 1035 (1995).
C. F. Daganzo, Requiem for second order fluid approximations of traffic flow, Transp. Research B, 29, (1995), 277–286.
R. Billot, C. Chalons, F. De Vuyst, N. E. El Faouzi, J. Sau, A conditionally linearly stable second-order traffic model derived from a Vlasov kinetic description, Comptes Rendus Mécanique, Volume 338 (9) (2010), 529–537.
D. Helbing and A. Johansson, On the controversy around DaganzoŠs requiem for and Aw-Rascle’s resurrection of 2nd-order traffic flow models, Eur. Phys. J. B 69(4), (2009), 549–562.
R. Illner, C. Kirchner and R. Pinnau, A Derivation of the Aw-Rascle traffic models from the Fokker-Planck type kinetic models, Quart. Appl. Math. 67, (2009), 39–45.
B.S. Kerner, Springer, Berlin, New York (2009).
E. Tomer, L. Safonov and S. Havlin, Presence of Many Stable Nonhomogeneous States in an Inertial Car-Following Model, Phys. Rev. Lett. 84 (2), 382Ű385 (2000).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
De Vuyst, F., Ricci, V., Salvarani, F. (2011). Nonlocal Second Order Vehicular Traffic Flow Models And Lagrange-Remap Finite Volumes. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_82
Download citation
DOI: https://doi.org/10.1007/978-3-642-20671-9_82
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20670-2
Online ISBN: 978-3-642-20671-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)