AbstractIn this paper, we study the Payne–Whitham (PW) model as a hyperbolic system of conservation laws with relaxation and are interested in its solution patterns when it is unstable. With numerical simulations, we observed the formation of clusters in the solutions. A cluster, which consists of a shock and a transition layer, is a “strong” traveling wave in the sense of Liu (Commun. Math. Phys. 108 (1987) 153), and its traveling speed is equal to that of the corresponding shock. The time-asymptotic structure of a transition layer is described by a first-order ordinary differential equation. We also found that, due to the instability of the PW model, we could not predict the number of clusters or the position, height, or width of each cluster. Our study also reveals the intricate relationship between the structure of vehicle clusters and the parameter c0.
The formation and structure of vehicle clusters in the Payne–Whitham traffic flow model
Transportation Research Part B: Methodological ; 37 , 3 ; 207-223
2002-01-08
17 pages
Article (Journal)
Electronic Resource
English
The formation and structure of vehicle clusters in the Payne-Whitham traffic flow model
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