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A Characteristic Particle Method for Traffic Flow Simulations on Highway Networks

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Meshfree Methods for Partial Differential Equations VI

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 89))

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Abstract

A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method particleclaw, which solves scalar one dimensional hyperbolic conservation laws exactly, except for a small error right around shocks. The method is generalized to nonlinear network flows, where particle approximations on the edges are suitably coupled together at the network nodes. It is demonstrated in numerical examples that the resulting particle method can approximate traffic jams accurately, while only devoting a few degrees of freedom to each edge of the network.

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Notes

  1. 1.

    Even though densities are commonly denoted by \(\rho \), here we use u, in order to express the fact that the numerical approach applies to more general network flows.

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Acknowledgements

Y. Farjoun was partially financed by the Spanish Ministry of Science and Innovation under grant FIS2008-04921-C02-01. The authors would like to acknowledge support by the National Science Foundation. B. Seibold was supported through grant DMS–1007899. In addition, B. Seibold wishes to acknowledge partial support by the National Science Foundation through grants DMS–0813648 and DMS–1115278. Y. Farjoun wishes to acknowledge partial support through grant DMS–0703937. In addition, Farjoun thanks Luis Bonilla at the UC3M and Rodolfo R. Rosales at MIT for providing a framework under which this work was done.

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Authors and Affiliations

  1. Broad Institute of MIT and Harvard, 7 Cambridge Center, Cambridge, MA, 02142, USA

    Yossi Farjoun

  2. Department of Mathematics, Temple University, 1805 North Broad Street, Philadelphia, PA, 19122, USA

    Benjamin Seibold

Authors
  1. Yossi Farjoun
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  2. Benjamin Seibold
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Correspondence to Yossi Farjoun .

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Editors and Affiliations

  1. , Institut für Numerische Simulation, Universität Bonn, Wegelerstr. 6, City, 53115, Germany

    Michael Griebel

  2. Institut für Parallele, und Verteilte Systeme, Universität Stuttgart, Universitätsstraße 38, Stuttgart, 70569, Germany

    Marc Alexander Schweitzer

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Farjoun, Y., Seibold, B. (2013). A Characteristic Particle Method for Traffic Flow Simulations on Highway Networks. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations VI. Lecture Notes in Computational Science and Engineering, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32979-1_13

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