| Title | The Chapman-Enskog Expansion: A Novel Approach to Hierarchical Extensions of Lighthill-Whitham Models |
| Authors | P. Nelson, Alexandros Sopasakis |
| Publication | Transportation and Traffic Theory. Proceedings of the 14th International Symposium on Transportation and Traffic Theory, Jerusalem, Israel, July, 1999 |
| Year | 1999 |
| Pages | 51 - 79 |
| Document type | Conference paper |
| Conference name | 14th International Symposium on Transportation and Traffic Theory (ISTTT14 1999) |
| Conference Date | 1999-07-20/1999-07-23 |
| Conference Location | Jerusalem, Israel |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Pergamon Press |
| Abstract 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. |
| ISBN/ISSN/Other | ISBN: 978-0-080-43448-3 |
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