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The pressureless limit of the Riemann solutions for the improved Aw–Rascle–Zhang traffic flow model with speed-density collaborative perception
Journal article   Peer reviewed

The pressureless limit of the Riemann solutions for the improved Aw–Rascle–Zhang traffic flow model with speed-density collaborative perception

Weifeng Jiang, Yanzhe Fan, Tingting Chen and Tong Li
Physics of fluids (1994), Vol.38(7), 076117
07/2026
DOI: 10.1063/5.0344065

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Abstract

In this paper, we study the pressureless limiting behaviors of the Riemann solutions for the improved Aw–Rascle–Zhang model with a logarithmic equation of state, which describes driver behavior with speed-density collaborative perception. We construct the Riemann solutions containing composite waves by using the “Liu-entropy” condition. Then we investigate the limiting dynamics of the Riemann solutions and demonstrate the formation of δ-shock waves and vacuum states as the pressure vanishes. Moreover, we quantitatively compare logarithmic gas, polytropic gas, and Chaplygin gas with respect to the singularity rates of density in their respective Riemann solutions. Finally, numerical simulations are performed to validate the theoretical results. Two highlights are noteworthy. First, composite waves do not persist as the pressure vanishes. Second, we find a new mechanism in cavitation formation that, as the pressure vanishes, the vacuum is formed only by the rarefaction wave dispersion, and is completely independent of the intermediate state of the Riemann solutions.

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