The Chapman-Enskog Expansion: A Novel Approach to Hierarchical Extensions of Lighthill-Whitham Models

Summary, in English

This paper suggests that the Payne models should not properly be regarded as the traffic flow analog of the Navier-Stokes equations of fluid dynamics. Further, the Chapman-Enskog asymptotic expansion in a small parameter is shown to lead to an alternate class of models that seem to have a more legitimate claim to that distinction. Details of this expansion, about the stable-flow equilibria of the Prigogine-Herman kinetic equation and in the case that the passing probability and relaxation time are constant, are presented to orders zero and one. The zero-order and first-order expansions correspond, respectively, to the Lighthill-Whitham (LWR) model and to the LWR model with a diffusive correction. These are suggested to be the correct traffic-flow analogs of, respectively, the Euler and Navier-Stokes equations of fluid dynamics. Results of a numerical simulation for a simple traffic-flow problem suggest that the diffusive term represents a correction to the LWR model that captures, to some extent, effects stemming from the fact that vehicles actually travel at various speeds.

• Författare: P. Nelson; Alexandros Sopasakis
• Redaktör: Avishai Ceder
• Publiceringsår: 1999
• Språk: Engelska
• Sidor: 51-79
• Publikation/Tidskrift/Serie: Transportation and Traffic Theory. Proceedings of the 14th International Symposium on Transportation and Traffic Theory, Jerusalem, Israel, July, 1999
• Dokumenttyp: Konferensbidrag
• Förlag: Pergamon Press Ltd.
• Ämne: Mathematics
• Conference name: 14th International Symposium on Transportation and Traffic Theory (ISTTT14 1999)
• Conference date: 1999-07-20 - 1999-07-23
• Conference place: Jerusalem, Israel
• Status: Published
• ISBN/ISSN/Övrigt: ISBN: 0-080-43448-7; ISBN: 978-0-080-43448-3