Delta-shocks and vacuums in Riemann solutions to the Umami Chaplygin Aw–Rascle model

Shiwei Li and Hui Wang

Chaos, Solitons & Fractals, 2024, vol. 188, issue C

Abstract: This paper is concerned with the formation of delta-shocks and vacuum states for zero-pressure Euler equations. With the introduction of the Umami Chaplygin gas, the Riemann problem for Aw–Rascle model with the reasonable flux-function is solved analytically. The three kinds of Riemann solutions involving the delta-shock are obtained. The generalized Rankine–Hugoniot relation and entropy condition for delta-shock are clarified. Under the entropy condition, the existence and uniqueness of the delta-shock solution are established by solving the generalized Rankine–Hugoniot relation. It is rigorously shown that as the Umami Chaplygin gas pressure and flux-function approach to zero simultaneously, the Riemann solutions of the considered model converge to these of the zero-pressure Euler equations. The numerical results support the theoretical analysis in the end.

Keywords: Aw–Rascle model; Umami Chaplygin gas; Delta-shock; Vacuum; Numerical results (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924010658

DOI: 10.1016/j.chaos.2024.115513

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