Enskog equations for traffic flow evaluated up to Navier-Stokes order
Abstract Similarly to the treatment of dense gases and granular flows, Enskog-like kinetic equations are formulated for the dynamics of unidirectional freeway traffic. From these we derive fluid-dynamic equations, which, in comparision with ordinary gases or fluids, contain additional terms due to t...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Helbing, Dirk [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1998 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 1998 |
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| Übergeordnetes Werk: |
Enthalten in: Granular matter - Springer-Verlag, 1998, 1(1998), 1 vom: Mai, Seite 21-31 |
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| Übergeordnetes Werk: |
volume:1 ; year:1998 ; number:1 ; month:05 ; pages:21-31 |
| Links: |
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| DOI / URN: |
10.1007/PL00010906 |
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| Katalog-ID: |
OLC2051638063 |
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| 520 | |a Abstract Similarly to the treatment of dense gases and granular flows, Enskog-like kinetic equations are formulated for the dynamics of unidirectional freeway traffic. From these we derive fluid-dynamic equations, which, in comparision with ordinary gases or fluids, contain additional terms due to the dissipative and anisotropic vehicle interactions. It is shown that velocity-dependent space requirements are needed for a realistic description of congested traffic situations and unstable traffic flow. Apart from a calculation of Euler order equations, we indicate how Navier-Stokes corrections could be obtained by means of the relaxation approximation. A linear instability analysis indicates that the Navier-Stokes equations show an additional instability, which is confirmed by simulations. Nevertheless, the Euler and Navier-Stokes equations give rise to similar stop-and-go waves in the non-linear regime. The relevance of the proposed methods and results for describing granular flows is outlined. | ||
| 650 | 4 | |a Traffic Flow | |
| 650 | 4 | |a Congested Traffic | |
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10.1007/PL00010906 doi (DE-627)OLC2051638063 (DE-He213)PL00010906-p DE-627 ger DE-627 rakwb eng 500 VZ 16,13 ssgn Helbing, Dirk verfasserin aut Enskog equations for traffic flow evaluated up to Navier-Stokes order 1998 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1998 Abstract Similarly to the treatment of dense gases and granular flows, Enskog-like kinetic equations are formulated for the dynamics of unidirectional freeway traffic. From these we derive fluid-dynamic equations, which, in comparision with ordinary gases or fluids, contain additional terms due to the dissipative and anisotropic vehicle interactions. It is shown that velocity-dependent space requirements are needed for a realistic description of congested traffic situations and unstable traffic flow. Apart from a calculation of Euler order equations, we indicate how Navier-Stokes corrections could be obtained by means of the relaxation approximation. A linear instability analysis indicates that the Navier-Stokes equations show an additional instability, which is confirmed by simulations. Nevertheless, the Euler and Navier-Stokes equations give rise to similar stop-and-go waves in the non-linear regime. The relevance of the proposed methods and results for describing granular flows is outlined. Traffic Flow Congested Traffic Space Requirement Granular Flow Linear Instability Treiber, Martin aut Enthalten in Granular matter Springer-Verlag, 1998 1(1998), 1 vom: Mai, Seite 21-31 (DE-627)247936057 (DE-600)1440788-7 (DE-576)068745206 1434-5021 nnns volume:1 year:1998 number:1 month:05 pages:21-31 https://doi.org/10.1007/PL00010906 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2014 GBV_ILN_2018 GBV_ILN_4277 AR 1 1998 1 05 21-31 |
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10.1007/PL00010906 doi (DE-627)OLC2051638063 (DE-He213)PL00010906-p DE-627 ger DE-627 rakwb eng 500 VZ 16,13 ssgn Helbing, Dirk verfasserin aut Enskog equations for traffic flow evaluated up to Navier-Stokes order 1998 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1998 Abstract Similarly to the treatment of dense gases and granular flows, Enskog-like kinetic equations are formulated for the dynamics of unidirectional freeway traffic. From these we derive fluid-dynamic equations, which, in comparision with ordinary gases or fluids, contain additional terms due to the dissipative and anisotropic vehicle interactions. It is shown that velocity-dependent space requirements are needed for a realistic description of congested traffic situations and unstable traffic flow. Apart from a calculation of Euler order equations, we indicate how Navier-Stokes corrections could be obtained by means of the relaxation approximation. A linear instability analysis indicates that the Navier-Stokes equations show an additional instability, which is confirmed by simulations. Nevertheless, the Euler and Navier-Stokes equations give rise to similar stop-and-go waves in the non-linear regime. The relevance of the proposed methods and results for describing granular flows is outlined. Traffic Flow Congested Traffic Space Requirement Granular Flow Linear Instability Treiber, Martin aut Enthalten in Granular matter Springer-Verlag, 1998 1(1998), 1 vom: Mai, Seite 21-31 (DE-627)247936057 (DE-600)1440788-7 (DE-576)068745206 1434-5021 nnns volume:1 year:1998 number:1 month:05 pages:21-31 https://doi.org/10.1007/PL00010906 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2014 GBV_ILN_2018 GBV_ILN_4277 AR 1 1998 1 05 21-31 |
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10.1007/PL00010906 doi (DE-627)OLC2051638063 (DE-He213)PL00010906-p DE-627 ger DE-627 rakwb eng 500 VZ 16,13 ssgn Helbing, Dirk verfasserin aut Enskog equations for traffic flow evaluated up to Navier-Stokes order 1998 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1998 Abstract Similarly to the treatment of dense gases and granular flows, Enskog-like kinetic equations are formulated for the dynamics of unidirectional freeway traffic. From these we derive fluid-dynamic equations, which, in comparision with ordinary gases or fluids, contain additional terms due to the dissipative and anisotropic vehicle interactions. It is shown that velocity-dependent space requirements are needed for a realistic description of congested traffic situations and unstable traffic flow. Apart from a calculation of Euler order equations, we indicate how Navier-Stokes corrections could be obtained by means of the relaxation approximation. A linear instability analysis indicates that the Navier-Stokes equations show an additional instability, which is confirmed by simulations. Nevertheless, the Euler and Navier-Stokes equations give rise to similar stop-and-go waves in the non-linear regime. The relevance of the proposed methods and results for describing granular flows is outlined. Traffic Flow Congested Traffic Space Requirement Granular Flow Linear Instability Treiber, Martin aut Enthalten in Granular matter Springer-Verlag, 1998 1(1998), 1 vom: Mai, Seite 21-31 (DE-627)247936057 (DE-600)1440788-7 (DE-576)068745206 1434-5021 nnns volume:1 year:1998 number:1 month:05 pages:21-31 https://doi.org/10.1007/PL00010906 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2014 GBV_ILN_2018 GBV_ILN_4277 AR 1 1998 1 05 21-31 |
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10.1007/PL00010906 doi (DE-627)OLC2051638063 (DE-He213)PL00010906-p DE-627 ger DE-627 rakwb eng 500 VZ 16,13 ssgn Helbing, Dirk verfasserin aut Enskog equations for traffic flow evaluated up to Navier-Stokes order 1998 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1998 Abstract Similarly to the treatment of dense gases and granular flows, Enskog-like kinetic equations are formulated for the dynamics of unidirectional freeway traffic. From these we derive fluid-dynamic equations, which, in comparision with ordinary gases or fluids, contain additional terms due to the dissipative and anisotropic vehicle interactions. It is shown that velocity-dependent space requirements are needed for a realistic description of congested traffic situations and unstable traffic flow. Apart from a calculation of Euler order equations, we indicate how Navier-Stokes corrections could be obtained by means of the relaxation approximation. A linear instability analysis indicates that the Navier-Stokes equations show an additional instability, which is confirmed by simulations. Nevertheless, the Euler and Navier-Stokes equations give rise to similar stop-and-go waves in the non-linear regime. The relevance of the proposed methods and results for describing granular flows is outlined. Traffic Flow Congested Traffic Space Requirement Granular Flow Linear Instability Treiber, Martin aut Enthalten in Granular matter Springer-Verlag, 1998 1(1998), 1 vom: Mai, Seite 21-31 (DE-627)247936057 (DE-600)1440788-7 (DE-576)068745206 1434-5021 nnns volume:1 year:1998 number:1 month:05 pages:21-31 https://doi.org/10.1007/PL00010906 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2014 GBV_ILN_2018 GBV_ILN_4277 AR 1 1998 1 05 21-31 |
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10.1007/PL00010906 doi (DE-627)OLC2051638063 (DE-He213)PL00010906-p DE-627 ger DE-627 rakwb eng 500 VZ 16,13 ssgn Helbing, Dirk verfasserin aut Enskog equations for traffic flow evaluated up to Navier-Stokes order 1998 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1998 Abstract Similarly to the treatment of dense gases and granular flows, Enskog-like kinetic equations are formulated for the dynamics of unidirectional freeway traffic. From these we derive fluid-dynamic equations, which, in comparision with ordinary gases or fluids, contain additional terms due to the dissipative and anisotropic vehicle interactions. It is shown that velocity-dependent space requirements are needed for a realistic description of congested traffic situations and unstable traffic flow. Apart from a calculation of Euler order equations, we indicate how Navier-Stokes corrections could be obtained by means of the relaxation approximation. A linear instability analysis indicates that the Navier-Stokes equations show an additional instability, which is confirmed by simulations. Nevertheless, the Euler and Navier-Stokes equations give rise to similar stop-and-go waves in the non-linear regime. The relevance of the proposed methods and results for describing granular flows is outlined. Traffic Flow Congested Traffic Space Requirement Granular Flow Linear Instability Treiber, Martin aut Enthalten in Granular matter Springer-Verlag, 1998 1(1998), 1 vom: Mai, Seite 21-31 (DE-627)247936057 (DE-600)1440788-7 (DE-576)068745206 1434-5021 nnns volume:1 year:1998 number:1 month:05 pages:21-31 https://doi.org/10.1007/PL00010906 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2014 GBV_ILN_2018 GBV_ILN_4277 AR 1 1998 1 05 21-31 |
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Abstract Similarly to the treatment of dense gases and granular flows, Enskog-like kinetic equations are formulated for the dynamics of unidirectional freeway traffic. From these we derive fluid-dynamic equations, which, in comparision with ordinary gases or fluids, contain additional terms due to the dissipative and anisotropic vehicle interactions. It is shown that velocity-dependent space requirements are needed for a realistic description of congested traffic situations and unstable traffic flow. Apart from a calculation of Euler order equations, we indicate how Navier-Stokes corrections could be obtained by means of the relaxation approximation. A linear instability analysis indicates that the Navier-Stokes equations show an additional instability, which is confirmed by simulations. Nevertheless, the Euler and Navier-Stokes equations give rise to similar stop-and-go waves in the non-linear regime. The relevance of the proposed methods and results for describing granular flows is outlined. © Springer-Verlag Berlin Heidelberg 1998 |
| abstractGer |
Abstract Similarly to the treatment of dense gases and granular flows, Enskog-like kinetic equations are formulated for the dynamics of unidirectional freeway traffic. From these we derive fluid-dynamic equations, which, in comparision with ordinary gases or fluids, contain additional terms due to the dissipative and anisotropic vehicle interactions. It is shown that velocity-dependent space requirements are needed for a realistic description of congested traffic situations and unstable traffic flow. Apart from a calculation of Euler order equations, we indicate how Navier-Stokes corrections could be obtained by means of the relaxation approximation. A linear instability analysis indicates that the Navier-Stokes equations show an additional instability, which is confirmed by simulations. Nevertheless, the Euler and Navier-Stokes equations give rise to similar stop-and-go waves in the non-linear regime. The relevance of the proposed methods and results for describing granular flows is outlined. © Springer-Verlag Berlin Heidelberg 1998 |
| abstract_unstemmed |
Abstract Similarly to the treatment of dense gases and granular flows, Enskog-like kinetic equations are formulated for the dynamics of unidirectional freeway traffic. From these we derive fluid-dynamic equations, which, in comparision with ordinary gases or fluids, contain additional terms due to the dissipative and anisotropic vehicle interactions. It is shown that velocity-dependent space requirements are needed for a realistic description of congested traffic situations and unstable traffic flow. Apart from a calculation of Euler order equations, we indicate how Navier-Stokes corrections could be obtained by means of the relaxation approximation. A linear instability analysis indicates that the Navier-Stokes equations show an additional instability, which is confirmed by simulations. Nevertheless, the Euler and Navier-Stokes equations give rise to similar stop-and-go waves in the non-linear regime. The relevance of the proposed methods and results for describing granular flows is outlined. © Springer-Verlag Berlin Heidelberg 1998 |
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Treiber, Martin |
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10.1007/PL00010906 |
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2024-07-04T04:55:50.921Z |
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