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

Nelson, P. and Sopasakis, Alexandros LU (1999) 14th International Symposium on Transportation and Traffic Theory (ISTTT14 1999) In Transportation and Traffic Theory. Proceedings of the 14th International Symposium on Transportation and Traffic Theory, Jerusalem, Israel, July, 1999 p.51-79
Abstract
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... (More)
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. (Less)
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author
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Transportation and Traffic Theory. Proceedings of the 14th International Symposium on Transportation and Traffic Theory, Jerusalem, Israel, July, 1999
editor
Ceder, Avishai
pages
29 pages
publisher
Pergamon
conference name
14th International Symposium on Transportation and Traffic Theory (ISTTT14 1999)
ISBN
0-080-43448-7
978-0-080-43448-3
language
English
LU publication?
no
id
10af7af7-9888-40a6-870a-ecd258686ead (old id 2201937)
date added to LUP
2012-01-03 14:34:25
date last changed
2016-06-29 09:09:28
@misc{10af7af7-9888-40a6-870a-ecd258686ead,
  abstract     = {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.},
  author       = {Nelson, P. and Sopasakis, Alexandros},
  editor       = {Ceder, Avishai},
  isbn         = {0-080-43448-7},
  language     = {eng},
  pages        = {51--79},
  publisher    = {ARRAY(0xa092710)},
  series       = {Transportation and Traffic Theory. Proceedings of the 14th International Symposium on Transportation and Traffic Theory, Jerusalem, Israel, July, 1999},
  title        = {The Chapman-Enskog Expansion: A Novel Approach to Hierarchical Extensions of Lighthill-Whitham Models},
  year         = {1999},
}