The Chapman-Enskog Expansion: A Novel Approach to Hierarchical Extensions of Lighthill-Whitham Models
(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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/2201937
- author
- Nelson, P. and Sopasakis, Alexandros ^{LU}
- publishing date
- 1999
- 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(0x9aef838)}, 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}, }