Characteristic Decomposition of the Two-Dimensional ARZ Traffic Flow System

Xin, Xiaoqing; Guo, Lihui

doi:10.1007/s40840-023-01468-4

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2023

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“…It consists of three first-order hyperbolic partial differential equations which describe the evolution of the vehicle density and of the two velocities in the plane. Other extensions of this model have been considered in [43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Symmetry Analysis for the 2D Aw-Rascle Traffic-Flow Model of Multi-Lane Motorways in the Euler and Lagrange Variables

Paliathanasis

2023

Symmetry

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A detailed symmetry analysis is performed for a microscopic model used to describe traffic flow in two-lane motorways. The traffic flow theory employed in this model is a two-dimensional extension of the Aw-Rascle theory. The flow parameters, including vehicle density, and vertical and horizontal velocities, are described by a system of first-order partial differential equations belonging to the family of hydrodynamic systems. This fluid-dynamics model is expressed in terms of the Euler and Lagrange variables. The admitted Lie point symmetries and the one-dimensional optimal system are determined for both sets of variables. It is found that the admitted symmetries for the two sets of variables form different Lie algebras, leading to distinct one-dimensional optimal systems. Finally, the Lie symmetries are utilized to derive new similarity closed-form solutions.

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Section: Introductionmentioning

confidence: 99%

Symmetry Analysis for the 2D Aw-Rascle Traffic-Flow Model of Multi-Lane Motorways in the Euler and Lagrange Variables

Paliathanasis

2023

Symmetry

View full text Add to dashboard Cite

show abstract

Characteristic Decomposition of the Two-Dimensional ARZ Traffic Flow System

Cited by 1 publication

References 27 publications

Symmetry Analysis for the 2D Aw-Rascle Traffic-Flow Model of Multi-Lane Motorways in the Euler and Lagrange Variables

Symmetry Analysis for the 2D Aw-Rascle Traffic-Flow Model of Multi-Lane Motorways in the Euler and Lagrange Variables

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